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<span class="kw">let </span><font color="Maroon" title="c1">k</font> be   <a href="ordinal1.html#V7" title="ORDINAL1:attr.7">natural</a>   <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">R</font> being  <a href="scmring1.html#V1" title="SCMRING1:attr.1">good</a>  <a href="funcsdom.html#NM1" title="FUNCSDOM:NM.1">Ring</a><br/> for <font color="Olive" title="b2">s1</font>, <font color="Olive" title="b3">s2</font>, <font color="Olive" title="b4">s</font> being  <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Olive" title="b1">R</font></span>)</span>  st not <font color="Olive" title="b1">R</font> is  <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a>  holds <br/>for <font color="Olive" title="b5">p</font> being  <a href="ami_1.html#V10" title="AMI_1:attr.10">autonomic</a>  <a href="ami_1.html#NM4" title="AMI_1:NM.4">FinPartState</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Olive" title="b1">R</font></span>)</span>  st  <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Olive" title="b1">R</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Olive" title="b5">p</font> &amp; <font color="Olive" title="b5">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">s1</font> &amp;  <a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Olive" title="b5">p</font>,<font color="Maroon" title="c1">k</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b3">s2</font> &amp; <font color="Olive" title="b4">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">s1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Olive" title="b3">s2</font></span>)</span> holds <br/>for <font color="Olive" title="b6">i</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>  holds <br/> ( <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Olive" title="b2">s1</font></span>)</span>,<font color="Olive" title="b2">s1</font>,<font color="Olive" title="b6">i</font></span>)</span></span>)</span> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c1">k</font>,<span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Olive" title="b1">R</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Olive" title="b3">s2</font></span>)</span>,<font color="Olive" title="b3">s2</font>,<font color="Olive" title="b6">i</font></span>)</span> &amp;  <a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Olive" title="b2">s1</font></span>)</span>,<font color="Olive" title="b2">s1</font>,<font color="Olive" title="b6">i</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Olive" title="b2">s1</font></span>)</span>,<font color="Olive" title="b2">s1</font>,<font color="Olive" title="b6">i</font></span>)</span></span>)</span>,<font color="Maroon" title="c1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Olive" title="b3">s2</font></span>)</span>,<font color="Olive" title="b3">s2</font>,<font color="Olive" title="b6">i</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Olive" title="b3">s2</font></span>)</span>,<font color="Olive" title="b3">s2</font>,<font color="Olive" title="b6">i</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Olive" title="b2">s1</font></span>)</span>,<font color="Olive" title="b2">s1</font>,<font color="Olive" title="b6">i</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Olive" title="b5">p</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Olive" title="b3">s2</font></span>)</span>,<font color="Olive" title="b3">s2</font>,<font color="Olive" title="b6">i</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Olive" title="b5">p</font>,<font color="Maroon" title="c1">k</font></span>)</span></span>)</span></span>)</span> &amp;  <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Olive" title="b4">s</font></span>)</span>,<font color="Olive" title="b4">s</font>,<font color="Olive" title="b6">i</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Olive" title="b3">s2</font></span>)</span>,<font color="Olive" title="b3">s2</font>,<font color="Olive" title="b6">i</font></span>)</span> )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">R</font> be   <a href="scmring1.html#V1" title="SCMRING1:attr.1">good</a>  <a href="funcsdom.html#NM1" title="FUNCSDOM:NM.1">Ring</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">s1</font>, <font color="Olive" title="b2">s2</font>, <font color="Olive" title="b3">s</font> being  <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span>  st not <font color="Maroon" title="c2">R</font> is  <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a>  holds <br/>for <font color="Olive" title="b4">p</font> being  <a href="ami_1.html#V10" title="AMI_1:attr.10">autonomic</a>  <a href="ami_1.html#NM4" title="AMI_1:NM.4">FinPartState</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span>  st  <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Olive" title="b4">p</font> &amp; <font color="Olive" title="b4">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">s1</font> &amp;  <a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Olive" title="b4">p</font>,<font color="Maroon" title="c1">k</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">s2</font> &amp; <font color="Olive" title="b3">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">s1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Olive" title="b2">s2</font></span>)</span> holds <br/>for <font color="Olive" title="b5">i</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>  holds <br/> ( <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Olive" title="b1">s1</font></span>)</span>,<font color="Olive" title="b1">s1</font>,<font color="Olive" title="b5">i</font></span>)</span></span>)</span> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c1">k</font>,<span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Olive" title="b2">s2</font></span>)</span>,<font color="Olive" title="b2">s2</font>,<font color="Olive" title="b5">i</font></span>)</span> &amp;  <a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Olive" title="b1">s1</font></span>)</span>,<font color="Olive" title="b1">s1</font>,<font color="Olive" title="b5">i</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Olive" title="b1">s1</font></span>)</span>,<font color="Olive" title="b1">s1</font>,<font color="Olive" title="b5">i</font></span>)</span></span>)</span>,<font color="Maroon" title="c1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Olive" title="b2">s2</font></span>)</span>,<font color="Olive" title="b2">s2</font>,<font color="Olive" title="b5">i</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Olive" title="b2">s2</font></span>)</span>,<font color="Olive" title="b2">s2</font>,<font color="Olive" title="b5">i</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Olive" title="b1">s1</font></span>)</span>,<font color="Olive" title="b1">s1</font>,<font color="Olive" title="b5">i</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Olive" title="b4">p</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Olive" title="b2">s2</font></span>)</span>,<font color="Olive" title="b2">s2</font>,<font color="Olive" title="b5">i</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Olive" title="b4">p</font>,<font color="Maroon" title="c1">k</font></span>)</span></span>)</span></span>)</span> &amp;  <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Olive" title="b3">s</font></span>)</span>,<font color="Olive" title="b3">s</font>,<font color="Olive" title="b5">i</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Olive" title="b2">s2</font></span>)</span>,<font color="Olive" title="b2">s2</font>,<font color="Olive" title="b5">i</font></span>)</span> )</span><br/><span class="kw">let </span><font color="Maroon" title="c3">s1</font>, <font color="Maroon" title="c4">s2</font>, <font color="Maroon" title="c5">s</font> be   <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( not <font color="Maroon" title="c2">R</font> is  <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a>  implies for <font color="Olive" title="b1">p</font> being  <a href="ami_1.html#V10" title="AMI_1:attr.10">autonomic</a>  <a href="ami_1.html#NM4" title="AMI_1:NM.4">FinPartState</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span>  st  <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Olive" title="b1">p</font> &amp; <font color="Olive" title="b1">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">s1</font> &amp;  <a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Olive" title="b1">p</font>,<font color="Maroon" title="c1">k</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">s2</font> &amp; <font color="Maroon" title="c5">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">s1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c4">s2</font></span>)</span> holds <br/>for <font color="Olive" title="b2">i</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>  holds <br/> ( <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Olive" title="b2">i</font></span>)</span></span>)</span> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c1">k</font>,<span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Olive" title="b2">i</font></span>)</span> &amp;  <a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Olive" title="b2">i</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Olive" title="b2">i</font></span>)</span></span>)</span>,<font color="Maroon" title="c1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Olive" title="b2">i</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Olive" title="b2">i</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Olive" title="b2">i</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Olive" title="b1">p</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Olive" title="b2">i</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Olive" title="b1">p</font>,<font color="Maroon" title="c1">k</font></span>)</span></span>)</span></span>)</span> &amp;  <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<font color="Olive" title="b2">i</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Olive" title="b2">i</font></span>)</span> ) )</span><br/>









<span class="kw">assume </span><a NAME="E1:36"/><span class="lab"><font color="Green" title="E23">A1</font></span>: 
not <font color="Maroon" title="c2">R</font> is  <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">p</font> being  <a href="ami_1.html#V10" title="AMI_1:attr.10">autonomic</a>  <a href="ami_1.html#NM4" title="AMI_1:NM.4">FinPartState</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span>  st  <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Olive" title="b1">p</font> &amp; <font color="Olive" title="b1">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">s1</font> &amp;  <a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Olive" title="b1">p</font>,<font color="Maroon" title="c1">k</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">s2</font> &amp; <font color="Maroon" title="c5">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">s1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c4">s2</font></span>)</span> holds <br/>for <font color="Olive" title="b2">i</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>  holds <br/> ( <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Olive" title="b2">i</font></span>)</span></span>)</span> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c1">k</font>,<span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Olive" title="b2">i</font></span>)</span> &amp;  <a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Olive" title="b2">i</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Olive" title="b2">i</font></span>)</span></span>)</span>,<font color="Maroon" title="c1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Olive" title="b2">i</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Olive" title="b2">i</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Olive" title="b2">i</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Olive" title="b1">p</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Olive" title="b2">i</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Olive" title="b1">p</font>,<font color="Maroon" title="c1">k</font></span>)</span></span>)</span></span>)</span> &amp;  <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<font color="Olive" title="b2">i</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Olive" title="b2">i</font></span>)</span> )</span><br/>

<span class="kw">let </span><font color="Maroon" title="c6">p</font> be   <a href="ami_1.html#V10" title="AMI_1:attr.10">autonomic</a>  <a href="ami_1.html#NM4" title="AMI_1:NM.4">FinPartState</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c6">p</font> &amp; <font color="Maroon" title="c6">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">s1</font> &amp;  <a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c1">k</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">s2</font> &amp; <font color="Maroon" title="c5">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">s1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c4">s2</font></span>)</span> implies for <font color="Olive" title="b1">i</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>  holds <br/> ( <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Olive" title="b1">i</font></span>)</span></span>)</span> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c1">k</font>,<span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Olive" title="b1">i</font></span>)</span> &amp;  <a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Olive" title="b1">i</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Olive" title="b1">i</font></span>)</span></span>)</span>,<font color="Maroon" title="c1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Olive" title="b1">i</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Olive" title="b1">i</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Olive" title="b1">i</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Olive" title="b1">i</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c1">k</font></span>)</span></span>)</span></span>)</span> &amp;  <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<font color="Olive" title="b1">i</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Olive" title="b1">i</font></span>)</span> ) )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E2:36"/><span class="lab"><font color="Green" title="E24">A2</font></span>: 
 <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c6">p</font>
 <span class="kw">and </span><br/><a NAME="E3:36"/><span class="lab"><font color="Green" title="E25">A3</font></span>: 
<font color="Maroon" title="c6">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">s1</font>
 <span class="kw">and </span><br/><a NAME="E4:36"/><span class="lab"><font color="Green" title="E26">A4</font></span>: 
 <a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c1">k</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">s2</font>
 <span class="kw">and </span><br/><a NAME="E5:36"/><span class="lab"><font color="Green" title="E27">A5</font></span>: 
<font color="Maroon" title="c5">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">s1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">i</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>  holds <br/> ( <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Olive" title="b1">i</font></span>)</span></span>)</span> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c1">k</font>,<span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Olive" title="b1">i</font></span>)</span> &amp;  <a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Olive" title="b1">i</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Olive" title="b1">i</font></span>)</span></span>)</span>,<font color="Maroon" title="c1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Olive" title="b1">i</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Olive" title="b1">i</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Olive" title="b1">i</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Olive" title="b1">i</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c1">k</font></span>)</span></span>)</span></span>)</span> &amp;  <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<font color="Olive" title="b1">i</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Olive" title="b1">i</font></span>)</span> )</span><br/>

<span class="kw">defpred </span><font color="Maroon">S<sub>1</sub></font>[   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> ] <span class="kw">means </span>( <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,$1</span>)</span></span>)</span> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c1">k</font>,<span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,$1</span>)</span> &amp;  <a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,$1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,$1</span>)</span></span>)</span>,<font color="Maroon" title="c1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,$1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,$1</span>)</span> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,$1</span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,$1</span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c1">k</font></span>)</span></span>)</span></span>)</span> &amp;  <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,$1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,$1</span>)</span> );<br/>
<a NAME="E6:36"/><span class="lab"><font color="Green" title="E28">A6</font></span>: 
not <font color="Maroon" title="c6">p</font> is  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>  <a href="relat_1.html#V4" title="RELAT_1:attr.4">-defined</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:36"><span class="lab"><font color="Green" title="E24">A2</font></span></a>, <a class="ref" href="ami_1.html#T109" title="AMI_1:th.109">AMI_1:109</a></span>;<br/>
<a NAME="E7:36"/><span class="lab"><font color="Green" title="E29">A7</font></span>: 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c6">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c3">s1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:36"><span class="lab"><font color="Green" title="E24">A2</font></span></a>, <a class="txt" href="#E3:36"><span class="lab"><font color="Green" title="E25">A3</font></span></a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></span>;<br/>
<a NAME="E8:36"/><span class="kw">then </span>
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c6">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#T13" title="AMI_1:th.13">AMI_1:13</a></span>;<br/>
<a NAME="E9:36"/><span class="kw">then </span><span class="lab"><font color="Green" title="E30">A8</font></span>: 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c6">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c6">p</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:36"><span class="lab"><font color="Green" title="E23">A1</font></span></a>, <a class="txt" href="#E3:36"><span class="lab"><font color="Green" title="E25">A3</font></span></a>, <a class="txt" href="#E6:36"><span class="lab"><font color="Green" title="E28">A6</font></span></a>, <a class="ref" href="scmring4.html#T27" target="_self" title="SCMRING4:th.27">Th27</a></span>;<br/>
<a NAME="E10:36"/><span class="lab"><font color="Green" title="E31">A9</font></span>: 
<font color="Maroon" title="c6">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">s</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:36"><span class="lab"><font color="Green" title="E25">A3</font></span></a>, <a class="txt" href="#E4:36"><span class="lab"><font color="Green" title="E26">A4</font></span></a>, <a class="txt" href="#E5:36"><span class="lab"><font color="Green" title="E27">A5</font></span></a>, <a class="ref" href="scmring4.html#T34" target="_self" title="SCMRING4:th.34">Th34</a></span>;<br/>
<a NAME="E11:36"/><span class="lab"><font color="Green" title="E32">A10</font></span>: 
for <font color="Olive" title="b1">i</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>   st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">i</font>] holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="36_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">set </span><font color="Maroon" title="c7">DPp</font> =  <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font>;<br/>
<span class="kw">let </span><font color="Maroon" title="c8">i</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c8">i</font>] implies <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1] )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:36_1"/><span class="lab"><font color="Green" title="E33">A11</font></span>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c1">k</font>,<span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Maroon" title="c8">i</font></span>)</span>
 <span class="kw">and </span><br/><a NAME="E2:36_1"/><span class="lab"><font color="Green" title="E34">A12</font></span>: 
 <a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span>,<font color="Maroon" title="c1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Maroon" title="c8">i</font></span>)</span>
 <span class="kw">and </span><br/><a NAME="E3:36_1"/><span class="lab"><font color="Green" title="E35">A13</font></span>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c1">k</font></span>)</span></span>)</span></span>)</span>
 <span class="kw">and </span><br/><a NAME="E4:36_1"/><span class="lab"><font color="Green" title="E36">A14</font></span>: 
 <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Maroon" title="c8">i</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1]</span><br/>

<span class="kw">set </span><font color="Maroon" title="c9">Cs2i1</font> =  <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c10">Cs3i</font> =  <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c8">i</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c11">Cs2i</font> =  <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Maroon" title="c8">i</font>;<br/>
<a NAME="E5:36_1"/><span class="lab"><font color="Green" title="E37">T</font></span>: 
 <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Maroon" title="c8">i</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#T123" title="AMI_1:th.123">AMI_1:123</a></span>;<br/>
<span class="lab"><font color="Green" title="E38">A15</font></span>:  <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> = 
 <a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Maroon" title="c8">i</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#T14" title="AMI_1:th.14">AMI_1:14</a></span>
<br/>.= 
 <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Maroon" title="c8">i</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:36_1"><span class="lab"><font color="Green" title="E37">T</font></span></a></span>
;<br/>
<div><span class="lab"><font color="Green" title="E39">A16</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="36_1_2"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c12">s</font> be   <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">d</font> being   <a href="scmring2.html#M1" title="SCMRING2:mode.1">Data-Location</a> of <font color="Maroon" title="c2">R</font> holds  <font color="Olive" title="b1">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c12">s</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c13">d</font> be    <a href="scmring2.html#M1" title="SCMRING2:mode.1">Data-Location</a> of <font color="Maroon" title="c2">R</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c13">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c12">s</font></span>)</span></span><br/><a NAME="E1:36_1_2"/>
<font color="Maroon" title="c13">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmring2.html#T1" title="SCMRING2:th.1">SCMRING2:1</a></span>;<br/><span class="kw">hence </span><a NAME="E2:36_1_2"/>
<font color="Maroon" title="c13">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c12">s</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmring4.html#T9" target="_self" title="SCMRING4:th.9">Th9</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<div><span class="lab"><font color="Green" title="E40">A17</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="36_1_3"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c12">d</font> be    <a href="scmring2.html#M1" title="SCMRING2:mode.1">Data-Location</a> of <font color="Maroon" title="c2">R</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c12">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c12">d</font></span><br/><a NAME="E1:36_1_3"/><span class="lab"><font color="Green" title="E41">A18</font></span>: 
<font color="Maroon" title="c12">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:36_1"><span class="lab"><font color="Green" title="E39">A16</font></span></a></span>;<br/><span class="kw">hence </span><span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c12">d</font> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#T70" title="FUNCT_1:th.70">FUNCT_1:70</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c12">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:36_1"><span class="lab"><font color="Green" title="E36">A14</font></span></a>, <a class="txt" href="#E1:36_1_3"><span class="lab"><font color="Green" title="E41">A18</font></span></a>, <a class="ref" href="funct_1.html#T70" title="FUNCT_1:th.70">FUNCT_1:70</a></span>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">set </span><font color="Maroon" title="c12">Cs1i1</font> =  <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c13">Cs1i</font> =  <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font>;<br/>
<a NAME="E9:36_1"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="partfun1.html#D4" title="PARTFUN1:def.4">PARTFUN1:def 4</a></span>;<br/>
<a NAME="E10:36_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E41">A19</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a> </span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmring4.html#T1" target="_self" title="SCMRING4:th.1">Th1</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c14">j</font> being   <a href="ordinal1.html#V7" title="ORDINAL1:attr.7">natural</a>   <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> <span class="kw"> such that </span><br/><a NAME="E12:36_1"/><span class="lab"><font color="Green" title="E42">A20</font></span>: 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span>,<font color="Maroon" title="c14">j</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="amistd_1.html#T26" title="AMISTD_1:th.26">AMISTD_1:26</a></span>;<br/>
<span class="lab"><font color="Green" title="E43">A21</font></span>:  <a href="scmnorm.html#K1" title="SCMNORM:func.1">succ</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c1">k</font>,<span class="p2">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span></span>)</span> = 
 <a href="scmnorm.html#K1" title="SCMNORM:func.1">succ</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <span class="p2">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c14">j</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:36_1"><span class="lab"><font color="Green" title="E42">A20</font></span></a>, <a class="ref" href="amistd_1.html#D13" title="AMISTD_1:def.13">AMISTD_1:def 13</a></span>
<br/>.= 
 <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c14">j</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmring3.html#T67" title="SCMRING3:th.67">SCMRING3:67</a></span>
<br/>.= 
 <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c14">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <span class="p2">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c14">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c1">k</font>,<span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="amistd_1.html#D13" title="AMISTD_1:def.13">AMISTD_1:def 13</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmnorm.html#K1" title="SCMNORM:func.1">succ</a> <span class="p2">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span></span>)</span> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c1">k</font>,<span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:36_1"><span class="lab"><font color="Green" title="E42">A20</font></span></a>, <a class="ref" href="scmring3.html#T67" title="SCMRING3:th.67">SCMRING3:67</a></span>
;<br/>
<div><span class="lab"><font color="Green" title="E44">A22</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="36_1_5"><span class="kw">now </span></a><div class="add"><span class="kw">reconsider </span><font color="Maroon" title="c15">loc</font> =  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>  ;<br/><span class="kw">assume </span><a NAME="E2:36_1_5"/><span class="lab"><font color="Green" title="E45">A23</font></span>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c1">k</font>,<span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span><br/><a NAME="E3:36_1_5"/><span class="lab"><font color="Green" title="E46">A24</font></span>: 
<font color="Maroon" title="c15">loc</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c6">p</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:36"><span class="lab"><font color="Green" title="E23">A1</font></span></a>, <a class="txt" href="#E3:36"><span class="lab"><font color="Green" title="E25">A3</font></span></a>, <a class="txt" href="#E6:36"><span class="lab"><font color="Green" title="E28">A6</font></span></a>, <a class="ref" href="scmring4.html#T27" target="_self" title="SCMRING4:th.27">Th27</a></span>;<br/><a NAME="E4:36_1_5"/>
 <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c6">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">p</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T88" title="RELAT_1:th.88">RELAT_1:88</a></span>;<br/><a NAME="E5:36_1_5"/><span class="kw">then </span><span class="lab"><font color="Green" title="E47">A25</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c6">p</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c6">p</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></span>;<br/><a NAME="E6:36_1_5"/><span class="kw">then </span>
<font color="Maroon" title="c15">loc</font> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c1">k</font>,<span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c1">k</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:36_1_5"><span class="lab"><font color="Green" title="E46">A24</font></span></a>, <a class="ref" href="amistd_2.html#T71" title="AMISTD_2:th.71">AMISTD_2:71</a></span>;<br/><span class="kw">then </span><span class="lab"><font color="Green" title="E48">A26</font></span>: <span class="p1">(<span class="default"><a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c1">k</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c15">loc</font> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c1">k</font>,<span class="p2">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span></span>)</span> = 
<font color="Maroon" title="c4">s2</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c15">loc</font> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c1">k</font>,<span class="p2">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:36"><span class="lab"><font color="Green" title="E26">A4</font></span></a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c15">loc</font> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c1">k</font>,<span class="p2">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#T54" title="AMI_1:th.54">AMI_1:54</a></span>
;<br/><a NAME="E8:36_1_5"/><span class="lab"><font color="Green" title="E49">Y</font></span>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c15">loc</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <font color="Maroon" title="c15">loc</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#T150" title="AMI_1:th.150">AMI_1:150</a></span>;<br/><a NAME="E9:36_1_5"/><span class="lab"><font color="Green" title="E50">Z</font></span>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#T150" title="AMI_1:th.150">AMI_1:150</a></span>;<br/> <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> = 
<font color="Maroon" title="c3">s1</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <font color="Maroon" title="c15">loc</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:36_1_5"><span class="lab"><font color="Green" title="E49">Y</font></span></a>, <a class="ref" href="ami_1.html#T54" title="AMI_1:th.54">AMI_1:54</a></span>
<br/>.= 
<font color="Maroon" title="c6">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c15">loc</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:36"><span class="lab"><font color="Green" title="E25">A3</font></span></a>, <a class="txt" href="#E3:36_1_5"><span class="lab"><font color="Green" title="E46">A24</font></span></a>, <a class="txt" href="#E5:36_1_5"><span class="lab"><font color="Green" title="E47">A25</font></span></a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></span>
;<br/><span class="kw">hence </span><a NAME="E11:36_1_5"/>
 <a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:36_1_5"><span class="lab"><font color="Green" title="E45">A23</font></span></a>, <a class="txt" href="#E3:36_1_5"><span class="lab"><font color="Green" title="E46">A24</font></span></a>, <a class="txt" href="#E7:36_1_5"><span class="lab"><font color="Green" title="E48">A26</font></span></a>, <a class="txt" href="#E9:36_1_5"><span class="lab"><font color="Green" title="E50">Z</font></span></a>, <a class="ref" href="amistd_2.html#T76" title="AMISTD_2:th.76">AMISTD_2:76</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<a NAME="E15:36_1"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="partfun1.html#D4" title="PARTFUN1:def.4">PARTFUN1:def 4</a></span>;<br/>
<a NAME="E16:36_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E45">A27</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a> </span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmring4.html#T1" target="_self" title="SCMRING4:th.1">Th1</a></span>;<br/>
<a NAME="E17:36_1"/>
 <a href="ami_1.html#K15" title="AMI_1:func.15">Data-Locations</a> <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmring2.html#T31" title="SCMRING2:th.31">SCMRING2:31</a></span>;<br/>
<a NAME="E18:36_1"/><span class="kw">then </span>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c6">p</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T90" title="RELAT_1:th.90">RELAT_1:90</a></span>;<br/>
<a NAME="E19:36_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E46">A28</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <span class="p3">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T10" title="XBOOLE_1:th.10">XBOOLE_1:10</a>, <a class="ref" href="xboole_1.html#T17" title="XBOOLE_1:th.17">XBOOLE_1:17</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c15">Cs3i1</font> =  <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>;<br/>
<a NAME="E20:36_1"/><span class="lab"><font color="Green" title="E47">A29</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmring4.html#T9" target="_self" title="SCMRING4:th.9">Th9</a></span>;<br/>
<a NAME="E21:36_1"/><span class="lab"><font color="Green" title="E48">A30</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmring4.html#T9" target="_self" title="SCMRING4:th.9">Th9</a></span>;<br/>
<a NAME="E22:36_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E49">A31</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmring4.html#T9" target="_self" title="SCMRING4:th.9">Th9</a></span>;<br/>
<a NAME="E23:36_1"/><span class="lab"><font color="Green" title="E50">A32</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmring4.html#T9" target="_self" title="SCMRING4:th.9">Th9</a></span>;<br/>
<div><span class="lab"><font color="Green" title="E51">A33</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="36_1_6"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c16">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c16">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c16">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c16">x</font> implies <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c16">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c16">x</font> )</span><br/><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:36_1_6"/><span class="lab"><font color="Green" title="E52">A34</font></span>: 
<font color="Maroon" title="c16">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>
 <span class="kw">and </span><br/><a NAME="E2:36_1_6"/><span class="lab"><font color="Green" title="E53">A35</font></span>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c16">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c16">x</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c16">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c16">x</font></span><br/><span class="kw">thus </span><span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c16">x</font> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c16">x</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:36_1_6"><span class="lab"><font color="Green" title="E52">A34</font></span></a>, <a class="txt" href="#E2:36_1_6"><span class="lab"><font color="Green" title="E53">A35</font></span></a>, <a class="ref" href="funct_1.html#T70" title="FUNCT_1:th.70">FUNCT_1:70</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c16">x</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:36_1"><span class="lab"><font color="Green" title="E48">A30</font></span></a>, <a class="txt" href="#E23:36_1"><span class="lab"><font color="Green" title="E50">A32</font></span></a>, <a class="txt" href="#E1:36_1_6"><span class="lab"><font color="Green" title="E52">A34</font></span></a>, <a class="ref" href="funct_1.html#T70" title="FUNCT_1:th.70">FUNCT_1:70</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<a NAME="E25:36_1"/><span class="lab"><font color="Green" title="E52">A36</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmring4.html#T9" target="_self" title="SCMRING4:th.9">Th9</a></span>;<br/>
<div><span class="lab"><font color="Green" title="E53">A37</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="36_1_7"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c16">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c16">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c16">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c16">x</font> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c16">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c16">x</font> implies <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c16">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c16">x</font> )</span><br/><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:36_1_7"/><span class="lab"><font color="Green" title="E54">A38</font></span>: 
<font color="Maroon" title="c16">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>
 <span class="kw">and </span><br/><a NAME="E2:36_1_7"/><span class="lab"><font color="Green" title="E55">A39</font></span>: 
( <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c16">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c16">x</font> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c16">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c16">x</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c16">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c16">x</font></span><br/><a NAME="E3:36_1_7"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c16">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c16">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E25:36_1"><span class="lab"><font color="Green" title="E52">A36</font></span></a>, <a class="txt" href="#E21:36_1"><span class="lab"><font color="Green" title="E48">A30</font></span></a>, <a class="txt" href="#E1:36_1_7"><span class="lab"><font color="Green" title="E54">A38</font></span></a>, <a class="ref" href="funct_1.html#T70" title="FUNCT_1:th.70">FUNCT_1:70</a></span>;<br/><span class="kw">hence </span><a NAME="E4:36_1_7"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c16">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c16">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:36_1"><span class="lab"><font color="Green" title="E36">A14</font></span></a>, <a class="txt" href="#E20:36_1"><span class="lab"><font color="Green" title="E47">A29</font></span></a>, <a class="txt" href="#E21:36_1"><span class="lab"><font color="Green" title="E48">A30</font></span></a>, <a class="txt" href="#E24:36_1"><span class="lab"><font color="Green" title="E51">A33</font></span></a>, <a class="txt" href="#E1:36_1_7"><span class="lab"><font color="Green" title="E54">A38</font></span></a>, <a class="txt" href="#E2:36_1_7"><span class="lab"><font color="Green" title="E55">A39</font></span></a>, <a class="ref" href="funct_1.html#T70" title="FUNCT_1:th.70">FUNCT_1:70</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<a NAME="E27:36_1"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="partfun1.html#D4" title="PARTFUN1:def.4">PARTFUN1:def 4</a></span>;<br/>
<a NAME="E28:36_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E54">A40</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a> </span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmring4.html#T1" target="_self" title="SCMRING4:th.1">Th1</a></span>;<br/>
<a NAME="E29:36_1"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="partfun1.html#D4" title="PARTFUN1:def.4">PARTFUN1:def 4</a></span>;<br/>
<a NAME="E30:36_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E55">A41</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <span class="p4">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a> </span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmring4.html#T1" target="_self" title="SCMRING4:th.1">Th1</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c16">I</font> =  <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span>;<br/>
<a NAME="E31:36_1"/><span class="lab"><font color="Green" title="E56">T</font></span>: 
 <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#T123" title="AMI_1:th.123">AMI_1:123</a></span>;<br/>
<span class="lab"><font color="Green" title="E57">A42</font></span>:  <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> = 
 <a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#T14" title="AMI_1:th.14">AMI_1:14</a></span>
<br/>.= 
 <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E31:36_1"><span class="lab"><font color="Green" title="E56">T</font></span></a></span>
;<br/>
<span class="lab"><font color="Green" title="E58">A43</font></span>:  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T90" title="RELAT_1:th.90">RELAT_1:90</a></span>
<br/>.= 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E28:36_1"><span class="lab"><font color="Green" title="E54">A40</font></span></a>, <a class="txt" href="#E19:36_1"><span class="lab"><font color="Green" title="E46">A28</font></span></a>, <a class="ref" href="xboole_1.html#T10" title="XBOOLE_1:th.10">XBOOLE_1:10</a>, <a class="ref" href="xboole_1.html#T28" title="XBOOLE_1:th.28">XBOOLE_1:28</a></span>
;<br/>
<span class="lab"><font color="Green" title="E59">A44</font></span>:  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T90" title="RELAT_1:th.90">RELAT_1:90</a></span>
<br/>.= 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:36_1"><span class="lab"><font color="Green" title="E41">A19</font></span></a>, <a class="txt" href="#E19:36_1"><span class="lab"><font color="Green" title="E46">A28</font></span></a>, <a class="ref" href="xboole_1.html#T10" title="XBOOLE_1:th.10">XBOOLE_1:10</a>, <a class="ref" href="xboole_1.html#T28" title="XBOOLE_1:th.28">XBOOLE_1:28</a></span>
;<br/>
<a NAME="E35:36_1"/><span class="lab"><font color="Green" title="E60">A45</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c1">k</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="amistd_2.html#T68" title="AMISTD_2:th.68">AMISTD_2:68</a></span>;<br/>
<span class="kw">then </span><span class="lab"><font color="Green" title="E61">A46</font></span>:  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p4">(<span class="default"><a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c1">k</font></span>)</span></span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T90" title="RELAT_1:th.90">RELAT_1:90</a></span>
<br/>.= 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E30:36_1"><span class="lab"><font color="Green" title="E55">A41</font></span></a>, <a class="txt" href="#E19:36_1"><span class="lab"><font color="Green" title="E46">A28</font></span></a>, <a class="ref" href="xboole_1.html#T10" title="XBOOLE_1:th.10">XBOOLE_1:10</a>, <a class="ref" href="xboole_1.html#T28" title="XBOOLE_1:th.28">XBOOLE_1:28</a></span>
;<br/>
<a NAME="E37:36_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E62">A47</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E34:36_1"><span class="lab"><font color="Green" title="E59">A44</font></span></a>, <a class="ref" href="amistd_2.html#T68" title="AMISTD_2:th.68">AMISTD_2:68</a></span>;<br/>
<span class="lab"><font color="Green" title="E63">A48</font></span>:  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p4">(<span class="default"><a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c1">k</font></span>)</span></span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E35:36_1"><span class="lab"><font color="Green" title="E60">A45</font></span></a>, <a class="ref" href="relat_1.html#T90" title="RELAT_1:th.90">RELAT_1:90</a></span>
<br/>.= 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:36_1"><span class="lab"><font color="Green" title="E45">A27</font></span></a>, <a class="txt" href="#E19:36_1"><span class="lab"><font color="Green" title="E46">A28</font></span></a>, <a class="ref" href="xboole_1.html#T10" title="XBOOLE_1:th.10">XBOOLE_1:10</a>, <a class="ref" href="xboole_1.html#T28" title="XBOOLE_1:th.28">XBOOLE_1:28</a></span>
;<br/>
<div><span class="lab"><font color="Green" title="E64">A49</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="36_1_13"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c17">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">d</font> being   <a href="scmring2.html#M1" title="SCMRING2:mode.1">Data-Location</a> of <font color="Maroon" title="c2">R</font>  st <font color="Olive" title="b1">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">x</font> &amp; <font color="Olive" title="b1">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Olive" title="b1">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Olive" title="b1">d</font> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Olive" title="b1">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Olive" title="b1">d</font> holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c17">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c17">x</font></span><br/><span class="kw">let </span><font color="Maroon" title="c18">d</font> be    <a href="scmring2.html#M1" title="SCMRING2:mode.1">Data-Location</a> of <font color="Maroon" title="c2">R</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c18">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">x</font> &amp; <font color="Maroon" title="c18">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c18">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c18">d</font> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c18">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c18">d</font> implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c17">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c17">x</font> )</span><br/><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:36_1_13"/><span class="lab"><font color="Green" title="E65">A50</font></span>: 
<font color="Maroon" title="c18">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">x</font>
 <span class="kw">and </span><br/><a NAME="E2:36_1_13"/><span class="lab"><font color="Green" title="E66">A51</font></span>: 
<font color="Maroon" title="c18">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span>
 <span class="kw">and </span><br/><a NAME="E3:36_1_13"/><span class="lab"><font color="Green" title="E67">A52</font></span>: 
( <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c18">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c18">d</font> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c18">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c18">d</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c17">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c17">x</font></span><br/><a NAME="E4:36_1_13"/><span class="lab"><font color="Green" title="E68">A53</font></span>: 
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c18">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c18">d</font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c18">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c18">d</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E35:36_1"><span class="lab"><font color="Green" title="E60">A45</font></span></a>, <a class="txt" href="#E33:36_1"><span class="lab"><font color="Green" title="E58">A43</font></span></a>, <a class="txt" href="#E38:36_1"><span class="lab"><font color="Green" title="E63">A48</font></span></a>, <a class="txt" href="#E2:36_1_13"><span class="lab"><font color="Green" title="E66">A51</font></span></a>, <a class="ref" href="funct_1.html#T70" title="FUNCT_1:th.70">FUNCT_1:70</a></span>;<br/><span class="kw">thus </span><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c17">x</font> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c18">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E34:36_1"><span class="lab"><font color="Green" title="E59">A44</font></span></a>, <a class="txt" href="#E1:36_1_13"><span class="lab"><font color="Green" title="E65">A50</font></span></a>, <a class="txt" href="#E2:36_1_13"><span class="lab"><font color="Green" title="E66">A51</font></span></a>, <a class="ref" href="funct_1.html#T70" title="FUNCT_1:th.70">FUNCT_1:70</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c17">x</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:36_1"><span class="lab"><font color="Green" title="E35">A13</font></span></a>, <a class="txt" href="#E35:36_1"><span class="lab"><font color="Green" title="E60">A45</font></span></a>, <a class="txt" href="#E36:36_1"><span class="lab"><font color="Green" title="E61">A46</font></span></a>, <a class="txt" href="#E1:36_1_13"><span class="lab"><font color="Green" title="E65">A50</font></span></a>, <a class="txt" href="#E2:36_1_13"><span class="lab"><font color="Green" title="E66">A51</font></span></a>, <a class="txt" href="#E3:36_1_13"><span class="lab"><font color="Green" title="E67">A52</font></span></a>, <a class="txt" href="#E4:36_1_13"><span class="lab"><font color="Green" title="E68">A53</font></span></a>, <a class="ref" href="funct_1.html#T70" title="FUNCT_1:th.70">FUNCT_1:70</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<div><span class="lab"><font color="Green" title="E65">A54</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="36_1_14"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c17">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">d</font> being   <a href="scmring2.html#M1" title="SCMRING2:mode.1">Data-Location</a> of <font color="Maroon" title="c2">R</font>  st <font color="Olive" title="b1">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">x</font> &amp; <font color="Olive" title="b1">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Olive" title="b1">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Olive" title="b1">d</font> holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c17">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c17">x</font></span><br/><span class="kw">let </span><font color="Maroon" title="c18">d</font> be    <a href="scmring2.html#M1" title="SCMRING2:mode.1">Data-Location</a> of <font color="Maroon" title="c2">R</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c18">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">x</font> &amp; <font color="Maroon" title="c18">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c18">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c18">d</font> implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c17">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c17">x</font> )</span><br/><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:36_1_14"/><span class="lab"><font color="Green" title="E66">A55</font></span>: 
( <font color="Maroon" title="c18">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">x</font> &amp; <font color="Maroon" title="c18">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span> )
 <span class="kw">and </span><br/><a NAME="E2:36_1_14"/><span class="lab"><font color="Green" title="E67">A56</font></span>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c18">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c18">d</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c17">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c17">x</font></span><br/><span class="kw">thus </span><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c17">x</font> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c18">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E34:36_1"><span class="lab"><font color="Green" title="E59">A44</font></span></a>, <a class="txt" href="#E1:36_1_14"><span class="lab"><font color="Green" title="E66">A55</font></span></a>, <a class="txt" href="#E2:36_1_14"><span class="lab"><font color="Green" title="E67">A56</font></span></a>, <a class="ref" href="funct_1.html#T70" title="FUNCT_1:th.70">FUNCT_1:70</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c17">x</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E35:36_1"><span class="lab"><font color="Green" title="E60">A45</font></span></a>, <a class="txt" href="#E36:36_1"><span class="lab"><font color="Green" title="E61">A46</font></span></a>, <a class="txt" href="#E1:36_1_14"><span class="lab"><font color="Green" title="E66">A55</font></span></a>, <a class="ref" href="funct_1.html#T70" title="FUNCT_1:th.70">FUNCT_1:70</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<a NAME="E41:36_1"/><span class="lab"><font color="Green" title="E66">T</font></span>: 
 <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c8">i</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#T123" title="AMI_1:th.123">AMI_1:123</a></span>;<br/>
<span class="lab"><font color="Green" title="E67">A57</font></span>:  <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> = 
 <a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c8">i</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#T14" title="AMI_1:th.14">AMI_1:14</a></span>
<br/>.= 
 <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c8">i</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:36"><span class="lab"><font color="Green" title="E23">A1</font></span></a>, <a class="txt" href="#E3:36"><span class="lab"><font color="Green" title="E25">A3</font></span></a>, <a class="txt" href="#E6:36"><span class="lab"><font color="Green" title="E28">A6</font></span></a>, <a class="txt" href="#E10:36"><span class="lab"><font color="Green" title="E31">A9</font></span></a>, <a class="ref" href="scmring4.html#T28" target="_self" title="SCMRING4:th.28">Th28</a>, <a class="txt" href="#E41:36_1"><span class="lab"><font color="Green" title="E66">T</font></span></a></span>
;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_1_16"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:36_1_16"/>
(  <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or  <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 or  <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 or  <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 or  <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 4 or  <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 5 or  <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 6 or  <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 7 )
 </span><span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T32" title="NAT_1:th.32">NAT_1:32</a>, <a class="ref" href="scmring3.html#T71" title="SCMRING3:th.71">SCMRING3:71</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_1_16_1"><span class="kw">suppose </span></a><a NAME="E1:36_1_16_1"/>
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1]</span><br/><div class="add"><a NAME="E2:36_1_16_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E68">A58</font></span>: 
 <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmring3.html#T16" title="SCMRING3:th.16">SCMRING3:16</a></span>;<br/><span class="kw">hence </span><span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c1">k</font>,<span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c1">k</font>,<span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E32:36_1"><span class="lab"><font color="Green" title="E57">A42</font></span></a>, <a class="ref" href="ami_1.html#D8" title="AMI_1:def.8">AMI_1:def 8</a></span>
<br/>.= 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:36_1"><span class="lab"><font color="Green" title="E33">A11</font></span></a>, <a class="txt" href="#E2:36_1"><span class="lab"><font color="Green" title="E34">A12</font></span></a>, <a class="txt" href="#E6:36_1"><span class="lab"><font color="Green" title="E38">A15</font></span></a>, <a class="txt" href="#E2:36_1_16_1"><span class="lab"><font color="Green" title="E68">A58</font></span></a>, <a class="ref" href="ami_1.html#D8" title="AMI_1:def.8">AMI_1:def 8</a></span>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c1">k</font></span>)</span></span>)</span></span>)</span> &amp;  <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> )</span><br/><span class="kw">hence </span><a NAME="E4:36_1_16_1"/>
 <a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:36_1"><span class="lab"><font color="Green" title="E44">A22</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c1">k</font></span>)</span></span>)</span></span>)</span> &amp;  <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> )</span><br/><a NAME="E5:36_1_16_1"/><span class="lab"><font color="Green" title="E69">A59</font></span>: 
 <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Maroon" title="c8">i</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:36_1"><span class="lab"><font color="Green" title="E34">A12</font></span></a>, <a class="txt" href="#E6:36_1"><span class="lab"><font color="Green" title="E38">A15</font></span></a>, <a class="txt" href="#E2:36_1_16_1"><span class="lab"><font color="Green" title="E68">A58</font></span></a>, <a class="ref" href="ami_1.html#D8" title="AMI_1:def.8">AMI_1:def 8</a></span>;<br/><span class="kw">hence </span><a NAME="E6:36_1_16_1"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c1">k</font></span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:36_1"><span class="lab"><font color="Green" title="E35">A13</font></span></a>, <a class="txt" href="#E32:36_1"><span class="lab"><font color="Green" title="E57">A42</font></span></a>, <a class="txt" href="#E2:36_1_16_1"><span class="lab"><font color="Green" title="E68">A58</font></span></a>, <a class="ref" href="ami_1.html#D8" title="AMI_1:def.8">AMI_1:def 8</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span><br/><span class="kw">thus </span><a NAME="E7:36_1_16_1"/>
 <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:36_1"><span class="lab"><font color="Green" title="E36">A14</font></span></a>, <a class="txt" href="#E42:36_1"><span class="lab"><font color="Green" title="E67">A57</font></span></a>, <a class="txt" href="#E2:36_1_16_1"><span class="lab"><font color="Green" title="E68">A58</font></span></a>, <a class="txt" href="#E5:36_1_16_1"><span class="lab"><font color="Green" title="E69">A59</font></span></a>, <a class="ref" href="ami_1.html#D8" title="AMI_1:def.8">AMI_1:def 8</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_1_16_2"><span class="kw">suppose </span></a><a NAME="E1:36_1_16_2"/>
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1]</span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c17">da</font>, <font color="Maroon" title="c18">db</font> being    <a href="scmring2.html#M1" title="SCMRING2:mode.1">Data-Location</a> of <font color="Maroon" title="c2">R</font><span class="kw"> such that </span><br/><a NAME="E3:36_1_16_2"/><span class="lab"><font color="Green" title="E68">A60</font></span>: 
 <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">da</font> <a href="scmring2.html#K4" title="SCMRING2:func.4">:=</a> <font color="Maroon" title="c18">db</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmring3.html#T17" title="SCMRING3:th.17">SCMRING3:17</a></span>;<br/><a NAME="E4:36_1_16_2"/><span class="lab"><font color="Green" title="E69">A61</font></span>: 
 <a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span>,<font color="Maroon" title="c1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">da</font> <a href="scmring2.html#K4" title="SCMRING2:func.4">:=</a> <font color="Maroon" title="c18">db</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:36_1_16_2"><span class="lab"><font color="Green" title="E68">A60</font></span></a>, <a class="ref" href="amistd_2.html#T29" title="AMISTD_2:th.29">AMISTD_2:29</a></span>;<br/><a NAME="E5:36_1_16_2"/><span class="lab"><font color="Green" title="E70">A62</font></span>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p4">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p5">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <span class="p2">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K1" title="SCMNORM:func.1">succ</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:36_1_16_2"><span class="lab"><font color="Green" title="E68">A60</font></span></a>, <a class="ref" href="scmring2.html#T13" title="SCMRING2:th.13">SCMRING2:13</a></span>;<br/><span class="kw">hence </span><a NAME="E6:36_1_16_2"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c1">k</font>,<span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:36_1"><span class="lab"><font color="Green" title="E33">A11</font></span></a>, <a class="txt" href="#E2:36_1"><span class="lab"><font color="Green" title="E34">A12</font></span></a>, <a class="txt" href="#E32:36_1"><span class="lab"><font color="Green" title="E57">A42</font></span></a>, <a class="txt" href="#E6:36_1"><span class="lab"><font color="Green" title="E38">A15</font></span></a>, <a class="txt" href="#E13:36_1"><span class="lab"><font color="Green" title="E43">A21</font></span></a>, <a class="txt" href="#E4:36_1_16_2"><span class="lab"><font color="Green" title="E69">A61</font></span></a>, <a class="ref" href="scmring2.html#T13" title="SCMRING2:th.13">SCMRING2:13</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c1">k</font></span>)</span></span>)</span></span>)</span> &amp;  <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> )</span><br/><span class="kw">thus </span><a NAME="E7:36_1_16_2"/>
 <a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:36_1"><span class="lab"><font color="Green" title="E33">A11</font></span></a>, <a class="txt" href="#E2:36_1"><span class="lab"><font color="Green" title="E34">A12</font></span></a>, <a class="txt" href="#E14:36_1"><span class="lab"><font color="Green" title="E44">A22</font></span></a>, <a class="txt" href="#E32:36_1"><span class="lab"><font color="Green" title="E57">A42</font></span></a>, <a class="txt" href="#E6:36_1"><span class="lab"><font color="Green" title="E38">A15</font></span></a>, <a class="txt" href="#E13:36_1"><span class="lab"><font color="Green" title="E43">A21</font></span></a>, <a class="txt" href="#E4:36_1_16_2"><span class="lab"><font color="Green" title="E69">A61</font></span></a>, <a class="txt" href="#E5:36_1_16_2"><span class="lab"><font color="Green" title="E70">A62</font></span></a>, <a class="ref" href="scmring2.html#T13" title="SCMRING2:th.13">SCMRING2:13</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c1">k</font></span>)</span></span>)</span></span>)</span> &amp;  <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> )</span><br/><a NAME="E8:36_1_16_2"/><span class="lab"><font color="Green" title="E71">A63</font></span>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c18">db</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c18">db</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:36_1"><span class="lab"><font color="Green" title="E40">A17</font></span></a></span>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="36_1_16_2_1"><span class="kw">now </span></a><div class="add"><a NAME="E1:36_1_16_2_1"/>
 <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">p</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T88" title="RELAT_1:th.88">RELAT_1:88</a></span>;<br/><a NAME="E2:36_1_16_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E72">A64</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c6">p</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></span>;<br/><span class="kw">let </span><font color="Maroon" title="c19">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> )</span><br/><span class="kw">assume </span><a NAME="E3:36_1_16_2_1"/><span class="lab"><font color="Green" title="E73">A65</font></span>: 
<font color="Maroon" title="c19">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><a NAME="E4:36_1_16_2_1"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmring4.html#T13" target="_self" title="SCMRING4:th.13">Th13</a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c20">d</font> = <font color="Maroon" title="c19">x</font> as    <a href="scmring2.html#M1" title="SCMRING2:mode.1">Data-Location</a> of <font color="Maroon" title="c2">R</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E34:36_1"><span class="lab"><font color="Green" title="E59">A44</font></span></a>, <a class="txt" href="#E3:36_1_16_2_1"><span class="lab"><font color="Green" title="E73">A65</font></span></a>, <a class="ref" href="scmring2.html#T1" title="SCMRING2:th.1">SCMRING2:1</a></span>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_1_16_2_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:36_1_16_2_1_1"/>
( <font color="Maroon" title="c17">da</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">d</font> or <font color="Maroon" title="c17">da</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c20">d</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_1_16_2_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:36_1_16_2_1_1_1"/><span class="lab"><font color="Green" title="E74">A66</font></span>: 
<font color="Maroon" title="c17">da</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">d</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><a NAME="E2:36_1_16_2_1_1_1"/><span class="kw">then </span>
( <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c20">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c18">db</font> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c20">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c18">db</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:36_1"><span class="lab"><font color="Green" title="E34">A12</font></span></a>, <a class="txt" href="#E32:36_1"><span class="lab"><font color="Green" title="E57">A42</font></span></a>, <a class="txt" href="#E6:36_1"><span class="lab"><font color="Green" title="E38">A15</font></span></a>, <a class="txt" href="#E3:36_1_16_2"><span class="lab"><font color="Green" title="E68">A60</font></span></a>, <a class="txt" href="#E4:36_1_16_2"><span class="lab"><font color="Green" title="E69">A61</font></span></a>, <a class="ref" href="scmring2.html#T13" title="SCMRING2:th.13">SCMRING2:13</a></span>;<br/><span class="kw">hence </span><a NAME="E3:36_1_16_2_1_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:36"><span class="lab"><font color="Green" title="E23">A1</font></span></a>, <a class="txt" href="#E3:36"><span class="lab"><font color="Green" title="E25">A3</font></span></a>, <a class="txt" href="#E6:36"><span class="lab"><font color="Green" title="E28">A6</font></span></a>, <a class="txt" href="#E10:36"><span class="lab"><font color="Green" title="E31">A9</font></span></a>, <a class="txt" href="#E34:36_1"><span class="lab"><font color="Green" title="E59">A44</font></span></a>, <a class="txt" href="#E40:36_1"><span class="lab"><font color="Green" title="E65">A54</font></span></a>, <a class="txt" href="#E3:36_1_16_2"><span class="lab"><font color="Green" title="E68">A60</font></span></a>, <a class="txt" href="#E8:36_1_16_2"><span class="lab"><font color="Green" title="E71">A63</font></span></a>, <a class="txt" href="#E3:36_1_16_2_1"><span class="lab"><font color="Green" title="E73">A65</font></span></a>, <a class="txt" href="#E2:36_1_16_2_1"><span class="lab"><font color="Green" title="E72">A64</font></span></a>, <a class="txt" href="#E1:36_1_16_2_1_1_1"><span class="lab"><font color="Green" title="E74">A66</font></span></a>, <a class="ref" href="scmring4.html#T29" target="_self" title="SCMRING4:th.29">Th29</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_1_16_2_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:36_1_16_2_1_1_2"/>
<font color="Maroon" title="c17">da</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c20">d</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><a NAME="E2:36_1_16_2_1_1_2"/><span class="kw">then </span>
( <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c20">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c20">d</font> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c20">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c20">d</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:36_1"><span class="lab"><font color="Green" title="E34">A12</font></span></a>, <a class="txt" href="#E32:36_1"><span class="lab"><font color="Green" title="E57">A42</font></span></a>, <a class="txt" href="#E6:36_1"><span class="lab"><font color="Green" title="E38">A15</font></span></a>, <a class="txt" href="#E3:36_1_16_2"><span class="lab"><font color="Green" title="E68">A60</font></span></a>, <a class="txt" href="#E4:36_1_16_2"><span class="lab"><font color="Green" title="E69">A61</font></span></a>, <a class="ref" href="scmring2.html#T13" title="SCMRING2:th.13">SCMRING2:13</a></span>;<br/><span class="kw">hence </span><a NAME="E3:36_1_16_2_1_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E34:36_1"><span class="lab"><font color="Green" title="E59">A44</font></span></a>, <a class="txt" href="#E39:36_1"><span class="lab"><font color="Green" title="E64">A49</font></span></a>, <a class="txt" href="#E3:36_1_16_2_1"><span class="lab"><font color="Green" title="E73">A65</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div><a NAME="E10:36_1_16_2"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E37:36_1"><span class="lab"><font color="Green" title="E62">A47</font></span></a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></span>;<br/><span class="kw">hence </span><a NAME="E11:36_1_16_2"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c1">k</font></span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E35:36_1"><span class="lab"><font color="Green" title="E60">A45</font></span></a>, <a class="txt" href="#E34:36_1"><span class="lab"><font color="Green" title="E59">A44</font></span></a>, <a class="txt" href="#E36:36_1"><span class="lab"><font color="Green" title="E61">A46</font></span></a>, <a class="ref" href="grfunc_1.html#T9" title="GRFUNC_1:th.9">GRFUNC_1:9</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span><br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="36_1_16_2_2"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c19">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> implies <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> )</span><br/><span class="kw">assume </span><a NAME="E1:36_1_16_2_2"/><span class="lab"><font color="Green" title="E72">A67</font></span>: 
<font color="Maroon" title="c19">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c20">d</font> = <font color="Maroon" title="c19">x</font> as    <a href="scmring2.html#M1" title="SCMRING2:mode.1">Data-Location</a> of <font color="Maroon" title="c2">R</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:36_1"><span class="lab"><font color="Green" title="E48">A30</font></span></a>, <a class="ref" href="scmring2.html#T1" title="SCMRING2:th.1">SCMRING2:1</a></span>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_1_16_2_2_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:36_1_16_2_2_1"/>
( <font color="Maroon" title="c17">da</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">d</font> or <font color="Maroon" title="c17">da</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c20">d</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_1_16_2_2_1_1"><span class="kw">suppose </span></a><a NAME="E1:36_1_16_2_2_1_1"/>
<font color="Maroon" title="c17">da</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">d</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><a NAME="E2:36_1_16_2_2_1_1"/><span class="kw">then </span>
( <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c20">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c18">db</font> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c20">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c18">db</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:36_1"><span class="lab"><font color="Green" title="E34">A12</font></span></a>, <a class="txt" href="#E6:36_1"><span class="lab"><font color="Green" title="E38">A15</font></span></a>, <a class="txt" href="#E42:36_1"><span class="lab"><font color="Green" title="E67">A57</font></span></a>, <a class="txt" href="#E3:36_1_16_2"><span class="lab"><font color="Green" title="E68">A60</font></span></a>, <a class="txt" href="#E4:36_1_16_2"><span class="lab"><font color="Green" title="E69">A61</font></span></a>, <a class="ref" href="scmring2.html#T13" title="SCMRING2:th.13">SCMRING2:13</a></span>;<br/><span class="kw">hence </span><a NAME="E3:36_1_16_2_2_1_1"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:36_1"><span class="lab"><font color="Green" title="E40">A17</font></span></a>, <a class="txt" href="#E24:36_1"><span class="lab"><font color="Green" title="E51">A33</font></span></a>, <a class="txt" href="#E1:36_1_16_2_2"><span class="lab"><font color="Green" title="E72">A67</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_1_16_2_2_1_2"><span class="kw">suppose </span></a><a NAME="E1:36_1_16_2_2_1_2"/>
<font color="Maroon" title="c17">da</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c20">d</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><a NAME="E2:36_1_16_2_2_1_2"/><span class="kw">then </span>
( <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c20">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c20">d</font> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c20">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c20">d</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:36_1"><span class="lab"><font color="Green" title="E34">A12</font></span></a>, <a class="txt" href="#E6:36_1"><span class="lab"><font color="Green" title="E38">A15</font></span></a>, <a class="txt" href="#E42:36_1"><span class="lab"><font color="Green" title="E67">A57</font></span></a>, <a class="txt" href="#E3:36_1_16_2"><span class="lab"><font color="Green" title="E68">A60</font></span></a>, <a class="txt" href="#E4:36_1_16_2"><span class="lab"><font color="Green" title="E69">A61</font></span></a>, <a class="ref" href="scmring2.html#T13" title="SCMRING2:th.13">SCMRING2:13</a></span>;<br/><span class="kw">hence </span><a NAME="E3:36_1_16_2_2_1_2"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E26:36_1"><span class="lab"><font color="Green" title="E53">A37</font></span></a>, <a class="txt" href="#E1:36_1_16_2_2"><span class="lab"><font color="Green" title="E72">A67</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div><a NAME="E13:36_1_16_2"/><span class="kw">then </span>
 <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:36_1"><span class="lab"><font color="Green" title="E49">A31</font></span></a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></span>;<br/><span class="kw">hence </span><a NAME="E14:36_1_16_2"/>
 <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:36_1"><span class="lab"><font color="Green" title="E48">A30</font></span></a>, <a class="txt" href="#E23:36_1"><span class="lab"><font color="Green" title="E50">A32</font></span></a>, <a class="ref" href="grfunc_1.html#T9" title="GRFUNC_1:th.9">GRFUNC_1:9</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_1_16_3"><span class="kw">suppose </span></a><a NAME="E1:36_1_16_3"/>
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1]</span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c17">da</font>, <font color="Maroon" title="c18">db</font> being    <a href="scmring2.html#M1" title="SCMRING2:mode.1">Data-Location</a> of <font color="Maroon" title="c2">R</font><span class="kw"> such that </span><br/><a NAME="E3:36_1_16_3"/><span class="lab"><font color="Green" title="E68">A68</font></span>: 
 <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmring2.html#K5" title="SCMRING2:func.5">AddTo</a> <font color="Maroon" title="c17">da</font>,<font color="Maroon" title="c18">db</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmring3.html#T18" title="SCMRING3:th.18">SCMRING3:18</a></span>;<br/><a NAME="E4:36_1_16_3"/><span class="lab"><font color="Green" title="E69">A69</font></span>: 
 <a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span>,<font color="Maroon" title="c1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmring2.html#K5" title="SCMRING2:func.5">AddTo</a> <font color="Maroon" title="c17">da</font>,<font color="Maroon" title="c18">db</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:36_1_16_3"><span class="lab"><font color="Green" title="E68">A68</font></span></a>, <a class="ref" href="amistd_2.html#T29" title="AMISTD_2:th.29">AMISTD_2:29</a></span>;<br/><a NAME="E5:36_1_16_3"/><span class="lab"><font color="Green" title="E70">A70</font></span>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p4">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p5">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <span class="p2">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K1" title="SCMNORM:func.1">succ</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:36_1_16_3"><span class="lab"><font color="Green" title="E68">A68</font></span></a>, <a class="ref" href="scmring2.html#T14" title="SCMRING2:th.14">SCMRING2:14</a></span>;<br/><span class="kw">hence </span><a NAME="E6:36_1_16_3"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c1">k</font>,<span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:36_1"><span class="lab"><font color="Green" title="E33">A11</font></span></a>, <a class="txt" href="#E2:36_1"><span class="lab"><font color="Green" title="E34">A12</font></span></a>, <a class="txt" href="#E32:36_1"><span class="lab"><font color="Green" title="E57">A42</font></span></a>, <a class="txt" href="#E6:36_1"><span class="lab"><font color="Green" title="E38">A15</font></span></a>, <a class="txt" href="#E13:36_1"><span class="lab"><font color="Green" title="E43">A21</font></span></a>, <a class="txt" href="#E4:36_1_16_3"><span class="lab"><font color="Green" title="E69">A69</font></span></a>, <a class="ref" href="scmring2.html#T14" title="SCMRING2:th.14">SCMRING2:14</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c1">k</font></span>)</span></span>)</span></span>)</span> &amp;  <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> )</span><br/><span class="kw">thus </span><a NAME="E7:36_1_16_3"/>
 <a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:36_1"><span class="lab"><font color="Green" title="E33">A11</font></span></a>, <a class="txt" href="#E2:36_1"><span class="lab"><font color="Green" title="E34">A12</font></span></a>, <a class="txt" href="#E14:36_1"><span class="lab"><font color="Green" title="E44">A22</font></span></a>, <a class="txt" href="#E32:36_1"><span class="lab"><font color="Green" title="E57">A42</font></span></a>, <a class="txt" href="#E6:36_1"><span class="lab"><font color="Green" title="E38">A15</font></span></a>, <a class="txt" href="#E13:36_1"><span class="lab"><font color="Green" title="E43">A21</font></span></a>, <a class="txt" href="#E4:36_1_16_3"><span class="lab"><font color="Green" title="E69">A69</font></span></a>, <a class="txt" href="#E5:36_1_16_3"><span class="lab"><font color="Green" title="E70">A70</font></span></a>, <a class="ref" href="scmring2.html#T14" title="SCMRING2:th.14">SCMRING2:14</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c1">k</font></span>)</span></span>)</span></span>)</span> &amp;  <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> )</span><br/><a NAME="E8:36_1_16_3"/><span class="lab"><font color="Green" title="E71">A71</font></span>: 
( <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c17">da</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c17">da</font> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c18">db</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c18">db</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:36_1"><span class="lab"><font color="Green" title="E40">A17</font></span></a></span>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="36_1_16_3_1"><span class="kw">now </span></a><div class="add"><a NAME="E1:36_1_16_3_1"/>
 <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">p</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T88" title="RELAT_1:th.88">RELAT_1:88</a></span>;<br/><a NAME="E2:36_1_16_3_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E72">A72</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c6">p</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></span>;<br/><span class="kw">let </span><font color="Maroon" title="c19">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> )</span><br/><span class="kw">assume </span><a NAME="E3:36_1_16_3_1"/><span class="lab"><font color="Green" title="E73">A73</font></span>: 
<font color="Maroon" title="c19">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><a NAME="E4:36_1_16_3_1"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmring4.html#T13" target="_self" title="SCMRING4:th.13">Th13</a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c20">d</font> = <font color="Maroon" title="c19">x</font> as    <a href="scmring2.html#M1" title="SCMRING2:mode.1">Data-Location</a> of <font color="Maroon" title="c2">R</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E34:36_1"><span class="lab"><font color="Green" title="E59">A44</font></span></a>, <a class="txt" href="#E3:36_1_16_3_1"><span class="lab"><font color="Green" title="E73">A73</font></span></a>, <a class="ref" href="scmring2.html#T1" title="SCMRING2:th.1">SCMRING2:1</a></span>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_1_16_3_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:36_1_16_3_1_1"/>
( <font color="Maroon" title="c17">da</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">d</font> or <font color="Maroon" title="c17">da</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c20">d</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_1_16_3_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:36_1_16_3_1_1_1"/><span class="lab"><font color="Green" title="E74">A74</font></span>: 
<font color="Maroon" title="c17">da</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">d</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><a NAME="E2:36_1_16_3_1_1_1"/><span class="kw">then </span>
( <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c20">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c17">da</font></span>)</span> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c18">db</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c20">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c17">da</font></span>)</span> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c18">db</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:36_1"><span class="lab"><font color="Green" title="E34">A12</font></span></a>, <a class="txt" href="#E32:36_1"><span class="lab"><font color="Green" title="E57">A42</font></span></a>, <a class="txt" href="#E6:36_1"><span class="lab"><font color="Green" title="E38">A15</font></span></a>, <a class="txt" href="#E3:36_1_16_3"><span class="lab"><font color="Green" title="E68">A68</font></span></a>, <a class="txt" href="#E4:36_1_16_3"><span class="lab"><font color="Green" title="E69">A69</font></span></a>, <a class="ref" href="scmring2.html#T14" title="SCMRING2:th.14">SCMRING2:14</a></span>;<br/><span class="kw">hence </span><a NAME="E3:36_1_16_3_1_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:36"><span class="lab"><font color="Green" title="E23">A1</font></span></a>, <a class="txt" href="#E3:36"><span class="lab"><font color="Green" title="E25">A3</font></span></a>, <a class="txt" href="#E6:36"><span class="lab"><font color="Green" title="E28">A6</font></span></a>, <a class="txt" href="#E10:36"><span class="lab"><font color="Green" title="E31">A9</font></span></a>, <a class="txt" href="#E34:36_1"><span class="lab"><font color="Green" title="E59">A44</font></span></a>, <a class="txt" href="#E40:36_1"><span class="lab"><font color="Green" title="E65">A54</font></span></a>, <a class="txt" href="#E3:36_1_16_3"><span class="lab"><font color="Green" title="E68">A68</font></span></a>, <a class="txt" href="#E8:36_1_16_3"><span class="lab"><font color="Green" title="E71">A71</font></span></a>, <a class="txt" href="#E3:36_1_16_3_1"><span class="lab"><font color="Green" title="E73">A73</font></span></a>, <a class="txt" href="#E2:36_1_16_3_1"><span class="lab"><font color="Green" title="E72">A72</font></span></a>, <a class="txt" href="#E1:36_1_16_3_1_1_1"><span class="lab"><font color="Green" title="E74">A74</font></span></a>, <a class="ref" href="scmring4.html#T30" target="_self" title="SCMRING4:th.30">Th30</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_1_16_3_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:36_1_16_3_1_1_2"/>
<font color="Maroon" title="c17">da</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c20">d</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><a NAME="E2:36_1_16_3_1_1_2"/><span class="kw">then </span>
( <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c20">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c20">d</font> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c20">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c20">d</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:36_1"><span class="lab"><font color="Green" title="E34">A12</font></span></a>, <a class="txt" href="#E32:36_1"><span class="lab"><font color="Green" title="E57">A42</font></span></a>, <a class="txt" href="#E6:36_1"><span class="lab"><font color="Green" title="E38">A15</font></span></a>, <a class="txt" href="#E3:36_1_16_3"><span class="lab"><font color="Green" title="E68">A68</font></span></a>, <a class="txt" href="#E4:36_1_16_3"><span class="lab"><font color="Green" title="E69">A69</font></span></a>, <a class="ref" href="scmring2.html#T14" title="SCMRING2:th.14">SCMRING2:14</a></span>;<br/><span class="kw">hence </span><a NAME="E3:36_1_16_3_1_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E34:36_1"><span class="lab"><font color="Green" title="E59">A44</font></span></a>, <a class="txt" href="#E39:36_1"><span class="lab"><font color="Green" title="E64">A49</font></span></a>, <a class="txt" href="#E3:36_1_16_3_1"><span class="lab"><font color="Green" title="E73">A73</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div><a NAME="E10:36_1_16_3"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E37:36_1"><span class="lab"><font color="Green" title="E62">A47</font></span></a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></span>;<br/><span class="kw">hence </span><a NAME="E11:36_1_16_3"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c1">k</font></span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E35:36_1"><span class="lab"><font color="Green" title="E60">A45</font></span></a>, <a class="txt" href="#E34:36_1"><span class="lab"><font color="Green" title="E59">A44</font></span></a>, <a class="txt" href="#E36:36_1"><span class="lab"><font color="Green" title="E61">A46</font></span></a>, <a class="ref" href="grfunc_1.html#T9" title="GRFUNC_1:th.9">GRFUNC_1:9</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span><br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="36_1_16_3_2"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c19">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> implies <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> )</span><br/><span class="kw">assume </span><a NAME="E1:36_1_16_3_2"/><span class="lab"><font color="Green" title="E72">A75</font></span>: 
<font color="Maroon" title="c19">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c20">d</font> = <font color="Maroon" title="c19">x</font> as    <a href="scmring2.html#M1" title="SCMRING2:mode.1">Data-Location</a> of <font color="Maroon" title="c2">R</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:36_1"><span class="lab"><font color="Green" title="E48">A30</font></span></a>, <a class="ref" href="scmring2.html#T1" title="SCMRING2:th.1">SCMRING2:1</a></span>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_1_16_3_2_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:36_1_16_3_2_1"/>
( <font color="Maroon" title="c17">da</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">d</font> or <font color="Maroon" title="c17">da</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c20">d</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_1_16_3_2_1_1"><span class="kw">suppose </span></a><a NAME="E1:36_1_16_3_2_1_1"/>
<font color="Maroon" title="c17">da</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">d</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><a NAME="E2:36_1_16_3_2_1_1"/><span class="kw">then </span>
( <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c20">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c17">da</font></span>)</span> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c18">db</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c20">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c17">da</font></span>)</span> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c18">db</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:36_1"><span class="lab"><font color="Green" title="E34">A12</font></span></a>, <a class="txt" href="#E6:36_1"><span class="lab"><font color="Green" title="E38">A15</font></span></a>, <a class="txt" href="#E42:36_1"><span class="lab"><font color="Green" title="E67">A57</font></span></a>, <a class="txt" href="#E3:36_1_16_3"><span class="lab"><font color="Green" title="E68">A68</font></span></a>, <a class="txt" href="#E4:36_1_16_3"><span class="lab"><font color="Green" title="E69">A69</font></span></a>, <a class="ref" href="scmring2.html#T14" title="SCMRING2:th.14">SCMRING2:14</a></span>;<br/><span class="kw">hence </span><a NAME="E3:36_1_16_3_2_1_1"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E24:36_1"><span class="lab"><font color="Green" title="E51">A33</font></span></a>, <a class="txt" href="#E8:36_1_16_3"><span class="lab"><font color="Green" title="E71">A71</font></span></a>, <a class="txt" href="#E1:36_1_16_3_2"><span class="lab"><font color="Green" title="E72">A75</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_1_16_3_2_1_2"><span class="kw">suppose </span></a><a NAME="E1:36_1_16_3_2_1_2"/>
<font color="Maroon" title="c17">da</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c20">d</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><a NAME="E2:36_1_16_3_2_1_2"/><span class="kw">then </span>
( <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c20">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c20">d</font> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c20">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c20">d</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:36_1"><span class="lab"><font color="Green" title="E34">A12</font></span></a>, <a class="txt" href="#E6:36_1"><span class="lab"><font color="Green" title="E38">A15</font></span></a>, <a class="txt" href="#E42:36_1"><span class="lab"><font color="Green" title="E67">A57</font></span></a>, <a class="txt" href="#E3:36_1_16_3"><span class="lab"><font color="Green" title="E68">A68</font></span></a>, <a class="txt" href="#E4:36_1_16_3"><span class="lab"><font color="Green" title="E69">A69</font></span></a>, <a class="ref" href="scmring2.html#T14" title="SCMRING2:th.14">SCMRING2:14</a></span>;<br/><span class="kw">hence </span><a NAME="E3:36_1_16_3_2_1_2"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E26:36_1"><span class="lab"><font color="Green" title="E53">A37</font></span></a>, <a class="txt" href="#E1:36_1_16_3_2"><span class="lab"><font color="Green" title="E72">A75</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div><a NAME="E13:36_1_16_3"/><span class="kw">then </span>
 <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:36_1"><span class="lab"><font color="Green" title="E49">A31</font></span></a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></span>;<br/><span class="kw">hence </span><a NAME="E14:36_1_16_3"/>
 <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:36_1"><span class="lab"><font color="Green" title="E48">A30</font></span></a>, <a class="txt" href="#E23:36_1"><span class="lab"><font color="Green" title="E50">A32</font></span></a>, <a class="ref" href="grfunc_1.html#T9" title="GRFUNC_1:th.9">GRFUNC_1:9</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_1_16_4"><span class="kw">suppose </span></a><a NAME="E1:36_1_16_4"/>
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1]</span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c17">da</font>, <font color="Maroon" title="c18">db</font> being    <a href="scmring2.html#M1" title="SCMRING2:mode.1">Data-Location</a> of <font color="Maroon" title="c2">R</font><span class="kw"> such that </span><br/><a NAME="E3:36_1_16_4"/><span class="lab"><font color="Green" title="E68">A76</font></span>: 
 <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmring2.html#K6" title="SCMRING2:func.6">SubFrom</a> <font color="Maroon" title="c17">da</font>,<font color="Maroon" title="c18">db</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmring3.html#T19" title="SCMRING3:th.19">SCMRING3:19</a></span>;<br/><a NAME="E4:36_1_16_4"/><span class="lab"><font color="Green" title="E69">A77</font></span>: 
 <a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span>,<font color="Maroon" title="c1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmring2.html#K6" title="SCMRING2:func.6">SubFrom</a> <font color="Maroon" title="c17">da</font>,<font color="Maroon" title="c18">db</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:36_1_16_4"><span class="lab"><font color="Green" title="E68">A76</font></span></a>, <a class="ref" href="amistd_2.html#T29" title="AMISTD_2:th.29">AMISTD_2:29</a></span>;<br/><a NAME="E5:36_1_16_4"/><span class="lab"><font color="Green" title="E70">A78</font></span>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p4">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p5">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <span class="p2">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K1" title="SCMNORM:func.1">succ</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:36_1_16_4"><span class="lab"><font color="Green" title="E68">A76</font></span></a>, <a class="ref" href="scmring2.html#T15" title="SCMRING2:th.15">SCMRING2:15</a></span>;<br/><span class="kw">hence </span><a NAME="E6:36_1_16_4"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c1">k</font>,<span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:36_1"><span class="lab"><font color="Green" title="E33">A11</font></span></a>, <a class="txt" href="#E2:36_1"><span class="lab"><font color="Green" title="E34">A12</font></span></a>, <a class="txt" href="#E32:36_1"><span class="lab"><font color="Green" title="E57">A42</font></span></a>, <a class="txt" href="#E6:36_1"><span class="lab"><font color="Green" title="E38">A15</font></span></a>, <a class="txt" href="#E13:36_1"><span class="lab"><font color="Green" title="E43">A21</font></span></a>, <a class="txt" href="#E4:36_1_16_4"><span class="lab"><font color="Green" title="E69">A77</font></span></a>, <a class="ref" href="scmring2.html#T15" title="SCMRING2:th.15">SCMRING2:15</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c1">k</font></span>)</span></span>)</span></span>)</span> &amp;  <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> )</span><br/><span class="kw">thus </span><a NAME="E7:36_1_16_4"/>
 <a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:36_1"><span class="lab"><font color="Green" title="E33">A11</font></span></a>, <a class="txt" href="#E2:36_1"><span class="lab"><font color="Green" title="E34">A12</font></span></a>, <a class="txt" href="#E14:36_1"><span class="lab"><font color="Green" title="E44">A22</font></span></a>, <a class="txt" href="#E32:36_1"><span class="lab"><font color="Green" title="E57">A42</font></span></a>, <a class="txt" href="#E6:36_1"><span class="lab"><font color="Green" title="E38">A15</font></span></a>, <a class="txt" href="#E13:36_1"><span class="lab"><font color="Green" title="E43">A21</font></span></a>, <a class="txt" href="#E4:36_1_16_4"><span class="lab"><font color="Green" title="E69">A77</font></span></a>, <a class="txt" href="#E5:36_1_16_4"><span class="lab"><font color="Green" title="E70">A78</font></span></a>, <a class="ref" href="scmring2.html#T15" title="SCMRING2:th.15">SCMRING2:15</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c1">k</font></span>)</span></span>)</span></span>)</span> &amp;  <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> )</span><br/><a NAME="E8:36_1_16_4"/><span class="lab"><font color="Green" title="E71">A79</font></span>: 
( <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c17">da</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c17">da</font> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c18">db</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c18">db</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:36_1"><span class="lab"><font color="Green" title="E40">A17</font></span></a></span>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="36_1_16_4_1"><span class="kw">now </span></a><div class="add"><a NAME="E1:36_1_16_4_1"/>
 <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">p</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T88" title="RELAT_1:th.88">RELAT_1:88</a></span>;<br/><a NAME="E2:36_1_16_4_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E72">A80</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c6">p</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></span>;<br/><span class="kw">let </span><font color="Maroon" title="c19">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> )</span><br/><span class="kw">assume </span><a NAME="E3:36_1_16_4_1"/><span class="lab"><font color="Green" title="E73">A81</font></span>: 
<font color="Maroon" title="c19">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><a NAME="E4:36_1_16_4_1"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmring4.html#T13" target="_self" title="SCMRING4:th.13">Th13</a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c20">d</font> = <font color="Maroon" title="c19">x</font> as    <a href="scmring2.html#M1" title="SCMRING2:mode.1">Data-Location</a> of <font color="Maroon" title="c2">R</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E34:36_1"><span class="lab"><font color="Green" title="E59">A44</font></span></a>, <a class="txt" href="#E3:36_1_16_4_1"><span class="lab"><font color="Green" title="E73">A81</font></span></a>, <a class="ref" href="scmring2.html#T1" title="SCMRING2:th.1">SCMRING2:1</a></span>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_1_16_4_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:36_1_16_4_1_1"/>
( <font color="Maroon" title="c17">da</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">d</font> or <font color="Maroon" title="c17">da</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c20">d</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_1_16_4_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:36_1_16_4_1_1_1"/><span class="lab"><font color="Green" title="E74">A82</font></span>: 
<font color="Maroon" title="c17">da</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">d</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><a NAME="E2:36_1_16_4_1_1_1"/><span class="kw">then </span>
( <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c20">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c17">da</font></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c18">db</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c20">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c17">da</font></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c18">db</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:36_1"><span class="lab"><font color="Green" title="E34">A12</font></span></a>, <a class="txt" href="#E32:36_1"><span class="lab"><font color="Green" title="E57">A42</font></span></a>, <a class="txt" href="#E6:36_1"><span class="lab"><font color="Green" title="E38">A15</font></span></a>, <a class="txt" href="#E3:36_1_16_4"><span class="lab"><font color="Green" title="E68">A76</font></span></a>, <a class="txt" href="#E4:36_1_16_4"><span class="lab"><font color="Green" title="E69">A77</font></span></a>, <a class="ref" href="scmring2.html#T15" title="SCMRING2:th.15">SCMRING2:15</a></span>;<br/><span class="kw">hence </span><a NAME="E3:36_1_16_4_1_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:36"><span class="lab"><font color="Green" title="E23">A1</font></span></a>, <a class="txt" href="#E3:36"><span class="lab"><font color="Green" title="E25">A3</font></span></a>, <a class="txt" href="#E6:36"><span class="lab"><font color="Green" title="E28">A6</font></span></a>, <a class="txt" href="#E10:36"><span class="lab"><font color="Green" title="E31">A9</font></span></a>, <a class="txt" href="#E34:36_1"><span class="lab"><font color="Green" title="E59">A44</font></span></a>, <a class="txt" href="#E40:36_1"><span class="lab"><font color="Green" title="E65">A54</font></span></a>, <a class="txt" href="#E3:36_1_16_4"><span class="lab"><font color="Green" title="E68">A76</font></span></a>, <a class="txt" href="#E8:36_1_16_4"><span class="lab"><font color="Green" title="E71">A79</font></span></a>, <a class="txt" href="#E3:36_1_16_4_1"><span class="lab"><font color="Green" title="E73">A81</font></span></a>, <a class="txt" href="#E2:36_1_16_4_1"><span class="lab"><font color="Green" title="E72">A80</font></span></a>, <a class="txt" href="#E1:36_1_16_4_1_1_1"><span class="lab"><font color="Green" title="E74">A82</font></span></a>, <a class="ref" href="scmring4.html#T31" target="_self" title="SCMRING4:th.31">Th31</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_1_16_4_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:36_1_16_4_1_1_2"/>
<font color="Maroon" title="c17">da</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c20">d</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><a NAME="E2:36_1_16_4_1_1_2"/><span class="kw">then </span>
( <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c20">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c20">d</font> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c20">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c20">d</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:36_1"><span class="lab"><font color="Green" title="E34">A12</font></span></a>, <a class="txt" href="#E32:36_1"><span class="lab"><font color="Green" title="E57">A42</font></span></a>, <a class="txt" href="#E6:36_1"><span class="lab"><font color="Green" title="E38">A15</font></span></a>, <a class="txt" href="#E3:36_1_16_4"><span class="lab"><font color="Green" title="E68">A76</font></span></a>, <a class="txt" href="#E4:36_1_16_4"><span class="lab"><font color="Green" title="E69">A77</font></span></a>, <a class="ref" href="scmring2.html#T15" title="SCMRING2:th.15">SCMRING2:15</a></span>;<br/><span class="kw">hence </span><a NAME="E3:36_1_16_4_1_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E34:36_1"><span class="lab"><font color="Green" title="E59">A44</font></span></a>, <a class="txt" href="#E39:36_1"><span class="lab"><font color="Green" title="E64">A49</font></span></a>, <a class="txt" href="#E3:36_1_16_4_1"><span class="lab"><font color="Green" title="E73">A81</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div><a NAME="E10:36_1_16_4"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E37:36_1"><span class="lab"><font color="Green" title="E62">A47</font></span></a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></span>;<br/><span class="kw">hence </span><a NAME="E11:36_1_16_4"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c1">k</font></span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E35:36_1"><span class="lab"><font color="Green" title="E60">A45</font></span></a>, <a class="txt" href="#E34:36_1"><span class="lab"><font color="Green" title="E59">A44</font></span></a>, <a class="txt" href="#E36:36_1"><span class="lab"><font color="Green" title="E61">A46</font></span></a>, <a class="ref" href="grfunc_1.html#T9" title="GRFUNC_1:th.9">GRFUNC_1:9</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span><br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="36_1_16_4_2"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c19">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> implies <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> )</span><br/><span class="kw">assume </span><a NAME="E1:36_1_16_4_2"/><span class="lab"><font color="Green" title="E72">A83</font></span>: 
<font color="Maroon" title="c19">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c20">d</font> = <font color="Maroon" title="c19">x</font> as    <a href="scmring2.html#M1" title="SCMRING2:mode.1">Data-Location</a> of <font color="Maroon" title="c2">R</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:36_1"><span class="lab"><font color="Green" title="E48">A30</font></span></a>, <a class="ref" href="scmring2.html#T1" title="SCMRING2:th.1">SCMRING2:1</a></span>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_1_16_4_2_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:36_1_16_4_2_1"/>
( <font color="Maroon" title="c17">da</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">d</font> or <font color="Maroon" title="c17">da</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c20">d</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_1_16_4_2_1_1"><span class="kw">suppose </span></a><a NAME="E1:36_1_16_4_2_1_1"/>
<font color="Maroon" title="c17">da</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">d</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><a NAME="E2:36_1_16_4_2_1_1"/><span class="kw">then </span>
( <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c20">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c17">da</font></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c18">db</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c20">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c17">da</font></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c18">db</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:36_1"><span class="lab"><font color="Green" title="E34">A12</font></span></a>, <a class="txt" href="#E6:36_1"><span class="lab"><font color="Green" title="E38">A15</font></span></a>, <a class="txt" href="#E42:36_1"><span class="lab"><font color="Green" title="E67">A57</font></span></a>, <a class="txt" href="#E3:36_1_16_4"><span class="lab"><font color="Green" title="E68">A76</font></span></a>, <a class="txt" href="#E4:36_1_16_4"><span class="lab"><font color="Green" title="E69">A77</font></span></a>, <a class="ref" href="scmring2.html#T15" title="SCMRING2:th.15">SCMRING2:15</a></span>;<br/><span class="kw">hence </span><a NAME="E3:36_1_16_4_2_1_1"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E24:36_1"><span class="lab"><font color="Green" title="E51">A33</font></span></a>, <a class="txt" href="#E8:36_1_16_4"><span class="lab"><font color="Green" title="E71">A79</font></span></a>, <a class="txt" href="#E1:36_1_16_4_2"><span class="lab"><font color="Green" title="E72">A83</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_1_16_4_2_1_2"><span class="kw">suppose </span></a><a NAME="E1:36_1_16_4_2_1_2"/>
<font color="Maroon" title="c17">da</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c20">d</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><a NAME="E2:36_1_16_4_2_1_2"/><span class="kw">then </span>
( <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c20">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c20">d</font> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c20">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c20">d</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:36_1"><span class="lab"><font color="Green" title="E34">A12</font></span></a>, <a class="txt" href="#E6:36_1"><span class="lab"><font color="Green" title="E38">A15</font></span></a>, <a class="txt" href="#E42:36_1"><span class="lab"><font color="Green" title="E67">A57</font></span></a>, <a class="txt" href="#E3:36_1_16_4"><span class="lab"><font color="Green" title="E68">A76</font></span></a>, <a class="txt" href="#E4:36_1_16_4"><span class="lab"><font color="Green" title="E69">A77</font></span></a>, <a class="ref" href="scmring2.html#T15" title="SCMRING2:th.15">SCMRING2:15</a></span>;<br/><span class="kw">hence </span><a NAME="E3:36_1_16_4_2_1_2"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E26:36_1"><span class="lab"><font color="Green" title="E53">A37</font></span></a>, <a class="txt" href="#E1:36_1_16_4_2"><span class="lab"><font color="Green" title="E72">A83</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div><a NAME="E13:36_1_16_4"/><span class="kw">then </span>
 <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:36_1"><span class="lab"><font color="Green" title="E49">A31</font></span></a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></span>;<br/><span class="kw">hence </span><a NAME="E14:36_1_16_4"/>
 <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:36_1"><span class="lab"><font color="Green" title="E48">A30</font></span></a>, <a class="txt" href="#E23:36_1"><span class="lab"><font color="Green" title="E50">A32</font></span></a>, <a class="ref" href="grfunc_1.html#T9" title="GRFUNC_1:th.9">GRFUNC_1:9</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_1_16_5"><span class="kw">suppose </span></a><a NAME="E1:36_1_16_5"/>
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 4
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1]</span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c17">da</font>, <font color="Maroon" title="c18">db</font> being    <a href="scmring2.html#M1" title="SCMRING2:mode.1">Data-Location</a> of <font color="Maroon" title="c2">R</font><span class="kw"> such that </span><br/><a NAME="E3:36_1_16_5"/><span class="lab"><font color="Green" title="E68">A84</font></span>: 
 <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmring2.html#K7" title="SCMRING2:func.7">MultBy</a> <font color="Maroon" title="c17">da</font>,<font color="Maroon" title="c18">db</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmring3.html#T20" title="SCMRING3:th.20">SCMRING3:20</a></span>;<br/><a NAME="E4:36_1_16_5"/><span class="lab"><font color="Green" title="E69">A85</font></span>: 
 <a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span>,<font color="Maroon" title="c1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmring2.html#K7" title="SCMRING2:func.7">MultBy</a> <font color="Maroon" title="c17">da</font>,<font color="Maroon" title="c18">db</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:36_1_16_5"><span class="lab"><font color="Green" title="E68">A84</font></span></a>, <a class="ref" href="amistd_2.html#T29" title="AMISTD_2:th.29">AMISTD_2:29</a></span>;<br/><a NAME="E5:36_1_16_5"/><span class="lab"><font color="Green" title="E70">A86</font></span>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p4">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p5">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <span class="p2">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K1" title="SCMNORM:func.1">succ</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:36_1_16_5"><span class="lab"><font color="Green" title="E68">A84</font></span></a>, <a class="ref" href="scmring2.html#T16" title="SCMRING2:th.16">SCMRING2:16</a></span>;<br/><span class="kw">hence </span><a NAME="E6:36_1_16_5"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c1">k</font>,<span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:36_1"><span class="lab"><font color="Green" title="E33">A11</font></span></a>, <a class="txt" href="#E2:36_1"><span class="lab"><font color="Green" title="E34">A12</font></span></a>, <a class="txt" href="#E32:36_1"><span class="lab"><font color="Green" title="E57">A42</font></span></a>, <a class="txt" href="#E6:36_1"><span class="lab"><font color="Green" title="E38">A15</font></span></a>, <a class="txt" href="#E13:36_1"><span class="lab"><font color="Green" title="E43">A21</font></span></a>, <a class="txt" href="#E4:36_1_16_5"><span class="lab"><font color="Green" title="E69">A85</font></span></a>, <a class="ref" href="scmring2.html#T16" title="SCMRING2:th.16">SCMRING2:16</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c1">k</font></span>)</span></span>)</span></span>)</span> &amp;  <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> )</span><br/><span class="kw">thus </span><a NAME="E7:36_1_16_5"/>
 <a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:36_1"><span class="lab"><font color="Green" title="E33">A11</font></span></a>, <a class="txt" href="#E2:36_1"><span class="lab"><font color="Green" title="E34">A12</font></span></a>, <a class="txt" href="#E14:36_1"><span class="lab"><font color="Green" title="E44">A22</font></span></a>, <a class="txt" href="#E32:36_1"><span class="lab"><font color="Green" title="E57">A42</font></span></a>, <a class="txt" href="#E6:36_1"><span class="lab"><font color="Green" title="E38">A15</font></span></a>, <a class="txt" href="#E13:36_1"><span class="lab"><font color="Green" title="E43">A21</font></span></a>, <a class="txt" href="#E4:36_1_16_5"><span class="lab"><font color="Green" title="E69">A85</font></span></a>, <a class="txt" href="#E5:36_1_16_5"><span class="lab"><font color="Green" title="E70">A86</font></span></a>, <a class="ref" href="scmring2.html#T16" title="SCMRING2:th.16">SCMRING2:16</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c1">k</font></span>)</span></span>)</span></span>)</span> &amp;  <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> )</span><br/><a NAME="E8:36_1_16_5"/><span class="lab"><font color="Green" title="E71">A87</font></span>: 
( <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c17">da</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c17">da</font> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c18">db</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c18">db</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:36_1"><span class="lab"><font color="Green" title="E40">A17</font></span></a></span>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="36_1_16_5_1"><span class="kw">now </span></a><div class="add"><a NAME="E1:36_1_16_5_1"/>
 <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">p</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T88" title="RELAT_1:th.88">RELAT_1:88</a></span>;<br/><a NAME="E2:36_1_16_5_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E72">A88</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c6">p</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></span>;<br/><span class="kw">let </span><font color="Maroon" title="c19">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> )</span><br/><span class="kw">assume </span><a NAME="E3:36_1_16_5_1"/><span class="lab"><font color="Green" title="E73">A89</font></span>: 
<font color="Maroon" title="c19">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><a NAME="E4:36_1_16_5_1"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmring4.html#T13" target="_self" title="SCMRING4:th.13">Th13</a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c20">d</font> = <font color="Maroon" title="c19">x</font> as    <a href="scmring2.html#M1" title="SCMRING2:mode.1">Data-Location</a> of <font color="Maroon" title="c2">R</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E34:36_1"><span class="lab"><font color="Green" title="E59">A44</font></span></a>, <a class="txt" href="#E3:36_1_16_5_1"><span class="lab"><font color="Green" title="E73">A89</font></span></a>, <a class="ref" href="scmring2.html#T1" title="SCMRING2:th.1">SCMRING2:1</a></span>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_1_16_5_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:36_1_16_5_1_1"/>
( <font color="Maroon" title="c17">da</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">d</font> or <font color="Maroon" title="c17">da</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c20">d</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_1_16_5_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:36_1_16_5_1_1_1"/><span class="lab"><font color="Green" title="E74">A90</font></span>: 
<font color="Maroon" title="c17">da</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">d</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><a NAME="E2:36_1_16_5_1_1_1"/><span class="kw">then </span>
( <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c20">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c17">da</font></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c18">db</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c20">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c17">da</font></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c18">db</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:36_1"><span class="lab"><font color="Green" title="E34">A12</font></span></a>, <a class="txt" href="#E32:36_1"><span class="lab"><font color="Green" title="E57">A42</font></span></a>, <a class="txt" href="#E6:36_1"><span class="lab"><font color="Green" title="E38">A15</font></span></a>, <a class="txt" href="#E3:36_1_16_5"><span class="lab"><font color="Green" title="E68">A84</font></span></a>, <a class="txt" href="#E4:36_1_16_5"><span class="lab"><font color="Green" title="E69">A85</font></span></a>, <a class="ref" href="scmring2.html#T16" title="SCMRING2:th.16">SCMRING2:16</a></span>;<br/><span class="kw">hence </span><a NAME="E3:36_1_16_5_1_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:36"><span class="lab"><font color="Green" title="E23">A1</font></span></a>, <a class="txt" href="#E3:36"><span class="lab"><font color="Green" title="E25">A3</font></span></a>, <a class="txt" href="#E6:36"><span class="lab"><font color="Green" title="E28">A6</font></span></a>, <a class="txt" href="#E10:36"><span class="lab"><font color="Green" title="E31">A9</font></span></a>, <a class="txt" href="#E34:36_1"><span class="lab"><font color="Green" title="E59">A44</font></span></a>, <a class="txt" href="#E40:36_1"><span class="lab"><font color="Green" title="E65">A54</font></span></a>, <a class="txt" href="#E3:36_1_16_5"><span class="lab"><font color="Green" title="E68">A84</font></span></a>, <a class="txt" href="#E8:36_1_16_5"><span class="lab"><font color="Green" title="E71">A87</font></span></a>, <a class="txt" href="#E3:36_1_16_5_1"><span class="lab"><font color="Green" title="E73">A89</font></span></a>, <a class="txt" href="#E2:36_1_16_5_1"><span class="lab"><font color="Green" title="E72">A88</font></span></a>, <a class="txt" href="#E1:36_1_16_5_1_1_1"><span class="lab"><font color="Green" title="E74">A90</font></span></a>, <a class="ref" href="scmring4.html#T32" target="_self" title="SCMRING4:th.32">Th32</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_1_16_5_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:36_1_16_5_1_1_2"/>
<font color="Maroon" title="c17">da</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c20">d</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><a NAME="E2:36_1_16_5_1_1_2"/><span class="kw">then </span>
( <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c20">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c20">d</font> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c20">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c20">d</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:36_1"><span class="lab"><font color="Green" title="E34">A12</font></span></a>, <a class="txt" href="#E32:36_1"><span class="lab"><font color="Green" title="E57">A42</font></span></a>, <a class="txt" href="#E6:36_1"><span class="lab"><font color="Green" title="E38">A15</font></span></a>, <a class="txt" href="#E3:36_1_16_5"><span class="lab"><font color="Green" title="E68">A84</font></span></a>, <a class="txt" href="#E4:36_1_16_5"><span class="lab"><font color="Green" title="E69">A85</font></span></a>, <a class="ref" href="scmring2.html#T16" title="SCMRING2:th.16">SCMRING2:16</a></span>;<br/><span class="kw">hence </span><a NAME="E3:36_1_16_5_1_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E34:36_1"><span class="lab"><font color="Green" title="E59">A44</font></span></a>, <a class="txt" href="#E39:36_1"><span class="lab"><font color="Green" title="E64">A49</font></span></a>, <a class="txt" href="#E3:36_1_16_5_1"><span class="lab"><font color="Green" title="E73">A89</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div><a NAME="E10:36_1_16_5"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E37:36_1"><span class="lab"><font color="Green" title="E62">A47</font></span></a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></span>;<br/><span class="kw">hence </span><a NAME="E11:36_1_16_5"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c1">k</font></span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E35:36_1"><span class="lab"><font color="Green" title="E60">A45</font></span></a>, <a class="txt" href="#E34:36_1"><span class="lab"><font color="Green" title="E59">A44</font></span></a>, <a class="txt" href="#E36:36_1"><span class="lab"><font color="Green" title="E61">A46</font></span></a>, <a class="ref" href="grfunc_1.html#T9" title="GRFUNC_1:th.9">GRFUNC_1:9</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span><br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="36_1_16_5_2"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c19">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> implies <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> )</span><br/><span class="kw">assume </span><a NAME="E1:36_1_16_5_2"/><span class="lab"><font color="Green" title="E72">A91</font></span>: 
<font color="Maroon" title="c19">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c20">d</font> = <font color="Maroon" title="c19">x</font> as    <a href="scmring2.html#M1" title="SCMRING2:mode.1">Data-Location</a> of <font color="Maroon" title="c2">R</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:36_1"><span class="lab"><font color="Green" title="E48">A30</font></span></a>, <a class="ref" href="scmring2.html#T1" title="SCMRING2:th.1">SCMRING2:1</a></span>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_1_16_5_2_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:36_1_16_5_2_1"/>
( <font color="Maroon" title="c17">da</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">d</font> or <font color="Maroon" title="c17">da</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c20">d</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_1_16_5_2_1_1"><span class="kw">suppose </span></a><a NAME="E1:36_1_16_5_2_1_1"/>
<font color="Maroon" title="c17">da</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">d</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><a NAME="E2:36_1_16_5_2_1_1"/><span class="kw">then </span>
( <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c20">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c17">da</font></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c18">db</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c20">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c17">da</font></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c18">db</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:36_1"><span class="lab"><font color="Green" title="E34">A12</font></span></a>, <a class="txt" href="#E6:36_1"><span class="lab"><font color="Green" title="E38">A15</font></span></a>, <a class="txt" href="#E42:36_1"><span class="lab"><font color="Green" title="E67">A57</font></span></a>, <a class="txt" href="#E3:36_1_16_5"><span class="lab"><font color="Green" title="E68">A84</font></span></a>, <a class="txt" href="#E4:36_1_16_5"><span class="lab"><font color="Green" title="E69">A85</font></span></a>, <a class="ref" href="scmring2.html#T16" title="SCMRING2:th.16">SCMRING2:16</a></span>;<br/><span class="kw">hence </span><a NAME="E3:36_1_16_5_2_1_1"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E24:36_1"><span class="lab"><font color="Green" title="E51">A33</font></span></a>, <a class="txt" href="#E8:36_1_16_5"><span class="lab"><font color="Green" title="E71">A87</font></span></a>, <a class="txt" href="#E1:36_1_16_5_2"><span class="lab"><font color="Green" title="E72">A91</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_1_16_5_2_1_2"><span class="kw">suppose </span></a><a NAME="E1:36_1_16_5_2_1_2"/>
<font color="Maroon" title="c17">da</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c20">d</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><a NAME="E2:36_1_16_5_2_1_2"/><span class="kw">then </span>
( <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c20">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c20">d</font> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c20">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c20">d</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:36_1"><span class="lab"><font color="Green" title="E34">A12</font></span></a>, <a class="txt" href="#E6:36_1"><span class="lab"><font color="Green" title="E38">A15</font></span></a>, <a class="txt" href="#E42:36_1"><span class="lab"><font color="Green" title="E67">A57</font></span></a>, <a class="txt" href="#E3:36_1_16_5"><span class="lab"><font color="Green" title="E68">A84</font></span></a>, <a class="txt" href="#E4:36_1_16_5"><span class="lab"><font color="Green" title="E69">A85</font></span></a>, <a class="ref" href="scmring2.html#T16" title="SCMRING2:th.16">SCMRING2:16</a></span>;<br/><span class="kw">hence </span><a NAME="E3:36_1_16_5_2_1_2"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E26:36_1"><span class="lab"><font color="Green" title="E53">A37</font></span></a>, <a class="txt" href="#E1:36_1_16_5_2"><span class="lab"><font color="Green" title="E72">A91</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div><a NAME="E13:36_1_16_5"/><span class="kw">then </span>
 <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:36_1"><span class="lab"><font color="Green" title="E49">A31</font></span></a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></span>;<br/><span class="kw">hence </span><a NAME="E14:36_1_16_5"/>
 <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:36_1"><span class="lab"><font color="Green" title="E48">A30</font></span></a>, <a class="txt" href="#E23:36_1"><span class="lab"><font color="Green" title="E50">A32</font></span></a>, <a class="ref" href="grfunc_1.html#T9" title="GRFUNC_1:th.9">GRFUNC_1:9</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_1_16_6"><span class="kw">suppose </span></a><a NAME="E1:36_1_16_6"/>
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 5
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1]</span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c17">da</font> being    <a href="scmring2.html#M1" title="SCMRING2:mode.1">Data-Location</a> of <font color="Maroon" title="c2">R</font>, <font color="Maroon" title="c18">r</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">R</font><span class="kw"> such that </span><br/><a NAME="E3:36_1_16_6"/><span class="lab"><font color="Green" title="E68">A92</font></span>: 
 <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">da</font> <a href="scmring2.html#K8" title="SCMRING2:func.8">:=</a> <font color="Maroon" title="c18">r</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmring3.html#T21" title="SCMRING3:th.21">SCMRING3:21</a></span>;<br/><a NAME="E4:36_1_16_6"/><span class="lab"><font color="Green" title="E69">A93</font></span>: 
 <a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span>,<font color="Maroon" title="c1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">da</font> <a href="scmring2.html#K8" title="SCMRING2:func.8">:=</a> <font color="Maroon" title="c18">r</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:36_1_16_6"><span class="lab"><font color="Green" title="E68">A92</font></span></a>, <a class="ref" href="amistd_2.html#T29" title="AMISTD_2:th.29">AMISTD_2:29</a></span>;<br/><a NAME="E5:36_1_16_6"/><span class="lab"><font color="Green" title="E70">A94</font></span>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p4">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p5">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <span class="p2">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K1" title="SCMNORM:func.1">succ</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:36_1_16_6"><span class="lab"><font color="Green" title="E68">A92</font></span></a>, <a class="ref" href="scmring2.html#T19" title="SCMRING2:th.19">SCMRING2:19</a></span>;<br/><span class="kw">hence </span><a NAME="E6:36_1_16_6"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c1">k</font>,<span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:36_1"><span class="lab"><font color="Green" title="E33">A11</font></span></a>, <a class="txt" href="#E2:36_1"><span class="lab"><font color="Green" title="E34">A12</font></span></a>, <a class="txt" href="#E32:36_1"><span class="lab"><font color="Green" title="E57">A42</font></span></a>, <a class="txt" href="#E6:36_1"><span class="lab"><font color="Green" title="E38">A15</font></span></a>, <a class="txt" href="#E13:36_1"><span class="lab"><font color="Green" title="E43">A21</font></span></a>, <a class="txt" href="#E4:36_1_16_6"><span class="lab"><font color="Green" title="E69">A93</font></span></a>, <a class="ref" href="scmring2.html#T19" title="SCMRING2:th.19">SCMRING2:19</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c1">k</font></span>)</span></span>)</span></span>)</span> &amp;  <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> )</span><br/><span class="kw">thus </span><a NAME="E7:36_1_16_6"/>
 <a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:36_1"><span class="lab"><font color="Green" title="E33">A11</font></span></a>, <a class="txt" href="#E2:36_1"><span class="lab"><font color="Green" title="E34">A12</font></span></a>, <a class="txt" href="#E14:36_1"><span class="lab"><font color="Green" title="E44">A22</font></span></a>, <a class="txt" href="#E32:36_1"><span class="lab"><font color="Green" title="E57">A42</font></span></a>, <a class="txt" href="#E6:36_1"><span class="lab"><font color="Green" title="E38">A15</font></span></a>, <a class="txt" href="#E13:36_1"><span class="lab"><font color="Green" title="E43">A21</font></span></a>, <a class="txt" href="#E4:36_1_16_6"><span class="lab"><font color="Green" title="E69">A93</font></span></a>, <a class="txt" href="#E5:36_1_16_6"><span class="lab"><font color="Green" title="E70">A94</font></span></a>, <a class="ref" href="scmring2.html#T19" title="SCMRING2:th.19">SCMRING2:19</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c1">k</font></span>)</span></span>)</span></span>)</span> &amp;  <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> )</span><br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="36_1_16_6_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c19">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> )</span><br/><span class="kw">assume </span><a NAME="E1:36_1_16_6_1"/><span class="lab"><font color="Green" title="E71">A95</font></span>: 
<font color="Maroon" title="c19">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><a NAME="E2:36_1_16_6_1"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmring4.html#T13" target="_self" title="SCMRING4:th.13">Th13</a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c20">d</font> = <font color="Maroon" title="c19">x</font> as    <a href="scmring2.html#M1" title="SCMRING2:mode.1">Data-Location</a> of <font color="Maroon" title="c2">R</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E34:36_1"><span class="lab"><font color="Green" title="E59">A44</font></span></a>, <a class="txt" href="#E1:36_1_16_6_1"><span class="lab"><font color="Green" title="E71">A95</font></span></a>, <a class="ref" href="scmring2.html#T1" title="SCMRING2:th.1">SCMRING2:1</a></span>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_1_16_6_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:36_1_16_6_1_1"/>
( <font color="Maroon" title="c17">da</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">d</font> or <font color="Maroon" title="c17">da</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c20">d</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_1_16_6_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:36_1_16_6_1_1_1"/><span class="lab"><font color="Green" title="E72">A96</font></span>: 
<font color="Maroon" title="c17">da</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">d</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><span class="kw">thus </span><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">x</font> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c20">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E34:36_1"><span class="lab"><font color="Green" title="E59">A44</font></span></a>, <a class="txt" href="#E1:36_1_16_6_1"><span class="lab"><font color="Green" title="E71">A95</font></span></a>, <a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></span>
<br/>.= 
<font color="Maroon" title="c18">r</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E32:36_1"><span class="lab"><font color="Green" title="E57">A42</font></span></a>, <a class="txt" href="#E3:36_1_16_6"><span class="lab"><font color="Green" title="E68">A92</font></span></a>, <a class="txt" href="#E1:36_1_16_6_1_1_1"><span class="lab"><font color="Green" title="E72">A96</font></span></a>, <a class="ref" href="scmring2.html#T19" title="SCMRING2:th.19">SCMRING2:19</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c20">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:36_1"><span class="lab"><font color="Green" title="E34">A12</font></span></a>, <a class="txt" href="#E6:36_1"><span class="lab"><font color="Green" title="E38">A15</font></span></a>, <a class="txt" href="#E4:36_1_16_6"><span class="lab"><font color="Green" title="E69">A93</font></span></a>, <a class="txt" href="#E1:36_1_16_6_1_1_1"><span class="lab"><font color="Green" title="E72">A96</font></span></a>, <a class="ref" href="scmring2.html#T19" title="SCMRING2:th.19">SCMRING2:19</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">x</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E34:36_1"><span class="lab"><font color="Green" title="E59">A44</font></span></a>, <a class="txt" href="#E1:36_1_16_6_1"><span class="lab"><font color="Green" title="E71">A95</font></span></a>, <a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_1_16_6_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:36_1_16_6_1_1_2"/>
<font color="Maroon" title="c17">da</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c20">d</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><a NAME="E2:36_1_16_6_1_1_2"/><span class="kw">then </span>
( <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c20">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c20">d</font> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c20">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c20">d</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:36_1"><span class="lab"><font color="Green" title="E34">A12</font></span></a>, <a class="txt" href="#E32:36_1"><span class="lab"><font color="Green" title="E57">A42</font></span></a>, <a class="txt" href="#E6:36_1"><span class="lab"><font color="Green" title="E38">A15</font></span></a>, <a class="txt" href="#E3:36_1_16_6"><span class="lab"><font color="Green" title="E68">A92</font></span></a>, <a class="txt" href="#E4:36_1_16_6"><span class="lab"><font color="Green" title="E69">A93</font></span></a>, <a class="ref" href="scmring2.html#T19" title="SCMRING2:th.19">SCMRING2:19</a></span>;<br/><span class="kw">hence </span><a NAME="E3:36_1_16_6_1_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E34:36_1"><span class="lab"><font color="Green" title="E59">A44</font></span></a>, <a class="txt" href="#E39:36_1"><span class="lab"><font color="Green" title="E64">A49</font></span></a>, <a class="txt" href="#E1:36_1_16_6_1"><span class="lab"><font color="Green" title="E71">A95</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div><a NAME="E9:36_1_16_6"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E37:36_1"><span class="lab"><font color="Green" title="E62">A47</font></span></a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></span>;<br/><span class="kw">hence </span><a NAME="E10:36_1_16_6"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c1">k</font></span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E35:36_1"><span class="lab"><font color="Green" title="E60">A45</font></span></a>, <a class="txt" href="#E34:36_1"><span class="lab"><font color="Green" title="E59">A44</font></span></a>, <a class="txt" href="#E36:36_1"><span class="lab"><font color="Green" title="E61">A46</font></span></a>, <a class="ref" href="grfunc_1.html#T9" title="GRFUNC_1:th.9">GRFUNC_1:9</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span><br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="36_1_16_6_2"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c19">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> implies <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> )</span><br/><span class="kw">assume </span><a NAME="E1:36_1_16_6_2"/><span class="lab"><font color="Green" title="E71">A97</font></span>: 
<font color="Maroon" title="c19">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c20">d</font> = <font color="Maroon" title="c19">x</font> as    <a href="scmring2.html#M1" title="SCMRING2:mode.1">Data-Location</a> of <font color="Maroon" title="c2">R</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:36_1"><span class="lab"><font color="Green" title="E48">A30</font></span></a>, <a class="ref" href="scmring2.html#T1" title="SCMRING2:th.1">SCMRING2:1</a></span>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_1_16_6_2_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:36_1_16_6_2_1"/>
( <font color="Maroon" title="c17">da</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">d</font> or <font color="Maroon" title="c17">da</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c20">d</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_1_16_6_2_1_1"><span class="kw">suppose </span></a><a NAME="E1:36_1_16_6_2_1_1"/>
<font color="Maroon" title="c17">da</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">d</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><a NAME="E2:36_1_16_6_2_1_1"/><span class="kw">then </span>
( <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c20">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">r</font> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c20">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">r</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:36_1"><span class="lab"><font color="Green" title="E34">A12</font></span></a>, <a class="txt" href="#E6:36_1"><span class="lab"><font color="Green" title="E38">A15</font></span></a>, <a class="txt" href="#E42:36_1"><span class="lab"><font color="Green" title="E67">A57</font></span></a>, <a class="txt" href="#E3:36_1_16_6"><span class="lab"><font color="Green" title="E68">A92</font></span></a>, <a class="txt" href="#E4:36_1_16_6"><span class="lab"><font color="Green" title="E69">A93</font></span></a>, <a class="ref" href="scmring2.html#T19" title="SCMRING2:th.19">SCMRING2:19</a></span>;<br/><span class="kw">hence </span><a NAME="E3:36_1_16_6_2_1_1"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E24:36_1"><span class="lab"><font color="Green" title="E51">A33</font></span></a>, <a class="txt" href="#E1:36_1_16_6_2"><span class="lab"><font color="Green" title="E71">A97</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_1_16_6_2_1_2"><span class="kw">suppose </span></a><a NAME="E1:36_1_16_6_2_1_2"/>
<font color="Maroon" title="c17">da</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c20">d</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><a NAME="E2:36_1_16_6_2_1_2"/><span class="kw">then </span>
( <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c20">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c20">d</font> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c20">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c20">d</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:36_1"><span class="lab"><font color="Green" title="E34">A12</font></span></a>, <a class="txt" href="#E6:36_1"><span class="lab"><font color="Green" title="E38">A15</font></span></a>, <a class="txt" href="#E42:36_1"><span class="lab"><font color="Green" title="E67">A57</font></span></a>, <a class="txt" href="#E3:36_1_16_6"><span class="lab"><font color="Green" title="E68">A92</font></span></a>, <a class="txt" href="#E4:36_1_16_6"><span class="lab"><font color="Green" title="E69">A93</font></span></a>, <a class="ref" href="scmring2.html#T19" title="SCMRING2:th.19">SCMRING2:19</a></span>;<br/><span class="kw">hence </span><a NAME="E3:36_1_16_6_2_1_2"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E26:36_1"><span class="lab"><font color="Green" title="E53">A37</font></span></a>, <a class="txt" href="#E1:36_1_16_6_2"><span class="lab"><font color="Green" title="E71">A97</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div><a NAME="E12:36_1_16_6"/><span class="kw">then </span>
 <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:36_1"><span class="lab"><font color="Green" title="E49">A31</font></span></a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></span>;<br/><span class="kw">hence </span><a NAME="E13:36_1_16_6"/>
 <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:36_1"><span class="lab"><font color="Green" title="E48">A30</font></span></a>, <a class="txt" href="#E23:36_1"><span class="lab"><font color="Green" title="E50">A32</font></span></a>, <a class="ref" href="grfunc_1.html#T9" title="GRFUNC_1:th.9">GRFUNC_1:9</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_1_16_7"><span class="kw">suppose </span></a><a NAME="E1:36_1_16_7"/>
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 6
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1]</span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c17">loc</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> <span class="kw"> such that </span><br/><a NAME="E3:36_1_16_7"/><span class="lab"><font color="Green" title="E68">A98</font></span>: 
 <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmring2.html#K9" title="SCMRING2:func.9">goto</a> <font color="Maroon" title="c17">loc</font>,<font color="Maroon" title="c2">R</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmring3.html#T22" title="SCMRING3:th.22">SCMRING3:22</a></span>;<br/><a NAME="E4:36_1_16_7"/><span class="lab"><font color="Green" title="E69">A99</font></span>: 
 <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmring2.html#K9" title="SCMRING2:func.9">goto</a> <span class="p1">(<span class="default"><font color="Maroon" title="c17">loc</font> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c1">k</font>,<span class="p2">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span></span>)</span>,<font color="Maroon" title="c2">R</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:36_1"><span class="lab"><font color="Green" title="E34">A12</font></span></a>, <a class="txt" href="#E3:36_1_16_7"><span class="lab"><font color="Green" title="E68">A98</font></span></a>, <a class="ref" href="scmring3.html#T69" title="SCMRING3:th.69">SCMRING3:69</a></span>;<br/><span class="kw">thus </span><span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c1">k</font>,<span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span> = 
<font color="Maroon" title="c17">loc</font> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c1">k</font>,<span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E32:36_1"><span class="lab"><font color="Green" title="E57">A42</font></span></a>, <a class="txt" href="#E3:36_1_16_7"><span class="lab"><font color="Green" title="E68">A98</font></span></a>, <a class="ref" href="scmring2.html#T17" title="SCMRING2:th.17">SCMRING2:17</a></span>
<br/>.= 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:36_1"><span class="lab"><font color="Green" title="E38">A15</font></span></a>, <a class="txt" href="#E4:36_1_16_7"><span class="lab"><font color="Green" title="E69">A99</font></span></a>, <a class="ref" href="scmring2.html#T17" title="SCMRING2:th.17">SCMRING2:17</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c1">k</font></span>)</span></span>)</span></span>)</span> &amp;  <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> )</span><br/><span class="kw">hence </span><a NAME="E6:36_1_16_7"/>
 <a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:36_1"><span class="lab"><font color="Green" title="E44">A22</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c1">k</font></span>)</span></span>)</span></span>)</span> &amp;  <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> )</span><br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="36_1_16_7_2"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c18">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c18">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c18">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c18">x</font> )</span><br/><span class="kw">assume </span><a NAME="E1:36_1_16_7_2"/><span class="lab"><font color="Green" title="E70">A100</font></span>: 
<font color="Maroon" title="c18">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c18">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c18">x</font></span><br/><a NAME="E2:36_1_16_7_2"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmring4.html#T13" target="_self" title="SCMRING4:th.13">Th13</a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c19">d</font> = <font color="Maroon" title="c18">x</font> as    <a href="scmring2.html#M1" title="SCMRING2:mode.1">Data-Location</a> of <font color="Maroon" title="c2">R</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E34:36_1"><span class="lab"><font color="Green" title="E59">A44</font></span></a>, <a class="txt" href="#E1:36_1_16_7_2"><span class="lab"><font color="Green" title="E70">A100</font></span></a>, <a class="ref" href="scmring2.html#T1" title="SCMRING2:th.1">SCMRING2:1</a></span>;<br/><a NAME="E4:36_1_16_7_2"/>
( <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c19">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c19">d</font> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c19">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c19">d</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E32:36_1"><span class="lab"><font color="Green" title="E57">A42</font></span></a>, <a class="txt" href="#E6:36_1"><span class="lab"><font color="Green" title="E38">A15</font></span></a>, <a class="txt" href="#E3:36_1_16_7"><span class="lab"><font color="Green" title="E68">A98</font></span></a>, <a class="txt" href="#E4:36_1_16_7"><span class="lab"><font color="Green" title="E69">A99</font></span></a>, <a class="ref" href="scmring2.html#T17" title="SCMRING2:th.17">SCMRING2:17</a></span>;<br/><span class="kw">hence </span><a NAME="E5:36_1_16_7_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c18">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c18">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E34:36_1"><span class="lab"><font color="Green" title="E59">A44</font></span></a>, <a class="txt" href="#E39:36_1"><span class="lab"><font color="Green" title="E64">A49</font></span></a>, <a class="txt" href="#E1:36_1_16_7_2"><span class="lab"><font color="Green" title="E70">A100</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><a NAME="E8:36_1_16_7"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E37:36_1"><span class="lab"><font color="Green" title="E62">A47</font></span></a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></span>;<br/><span class="kw">hence </span><a NAME="E9:36_1_16_7"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c1">k</font></span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E35:36_1"><span class="lab"><font color="Green" title="E60">A45</font></span></a>, <a class="txt" href="#E34:36_1"><span class="lab"><font color="Green" title="E59">A44</font></span></a>, <a class="txt" href="#E36:36_1"><span class="lab"><font color="Green" title="E61">A46</font></span></a>, <a class="ref" href="grfunc_1.html#T9" title="GRFUNC_1:th.9">GRFUNC_1:9</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span><br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="36_1_16_7_3"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c18">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c18">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> implies <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c18">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c18">x</font> )</span><br/><span class="kw">assume </span><a NAME="E1:36_1_16_7_3"/><span class="lab"><font color="Green" title="E70">A101</font></span>: 
<font color="Maroon" title="c18">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c18">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c18">x</font></span><br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c19">d</font> = <font color="Maroon" title="c18">x</font> as    <a href="scmring2.html#M1" title="SCMRING2:mode.1">Data-Location</a> of <font color="Maroon" title="c2">R</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:36_1"><span class="lab"><font color="Green" title="E48">A30</font></span></a>, <a class="ref" href="scmring2.html#T1" title="SCMRING2:th.1">SCMRING2:1</a></span>;<br/><a NAME="E3:36_1_16_7_3"/>
( <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c19">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c19">d</font> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c19">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c19">d</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:36_1"><span class="lab"><font color="Green" title="E38">A15</font></span></a>, <a class="txt" href="#E42:36_1"><span class="lab"><font color="Green" title="E67">A57</font></span></a>, <a class="txt" href="#E3:36_1_16_7"><span class="lab"><font color="Green" title="E68">A98</font></span></a>, <a class="txt" href="#E4:36_1_16_7"><span class="lab"><font color="Green" title="E69">A99</font></span></a>, <a class="ref" href="scmring2.html#T17" title="SCMRING2:th.17">SCMRING2:17</a></span>;<br/><span class="kw">hence </span><a NAME="E4:36_1_16_7_3"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c18">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c18">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E26:36_1"><span class="lab"><font color="Green" title="E53">A37</font></span></a>, <a class="txt" href="#E1:36_1_16_7_3"><span class="lab"><font color="Green" title="E70">A101</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><a NAME="E11:36_1_16_7"/><span class="kw">then </span>
 <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:36_1"><span class="lab"><font color="Green" title="E49">A31</font></span></a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></span>;<br/><span class="kw">hence </span><a NAME="E12:36_1_16_7"/>
 <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:36_1"><span class="lab"><font color="Green" title="E48">A30</font></span></a>, <a class="txt" href="#E23:36_1"><span class="lab"><font color="Green" title="E50">A32</font></span></a>, <a class="ref" href="grfunc_1.html#T9" title="GRFUNC_1:th.9">GRFUNC_1:9</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_1_16_8"><span class="kw">suppose </span></a><a NAME="E1:36_1_16_8"/>
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 7
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1]</span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c17">da</font> being    <a href="scmring2.html#M1" title="SCMRING2:mode.1">Data-Location</a> of <font color="Maroon" title="c2">R</font>, <font color="Maroon" title="c18">loc</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> <span class="kw"> such that </span><br/><a NAME="E3:36_1_16_8"/><span class="lab"><font color="Green" title="E68">A102</font></span>: 
 <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">da</font> <a href="scmring2.html#K10" title="SCMRING2:func.10">=0_goto</a> <font color="Maroon" title="c18">loc</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmring3.html#T23" title="SCMRING3:th.23">SCMRING3:23</a></span>;<br/><div><span class="lab"><font color="Green" title="E69">A103</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="36_1_16_8_1"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_1_16_8_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:36_1_16_8_1_1"/>
( <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c17">da</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">R</font> or <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c17">da</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">R</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_1_16_8_1_1_1"><span class="kw">case </span></a><a NAME="E1:36_1_16_8_1_1_1"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c17">da</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">R</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">loc</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:36_1_16_8_1_1_1"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">loc</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">k</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E32:36_1"><span class="lab"><font color="Green" title="E57">A42</font></span></a>, <a class="txt" href="#E3:36_1_16_8"><span class="lab"><font color="Green" title="E68">A102</font></span></a>, <a class="ref" href="scmring2.html#T18" title="SCMRING2:th.18">SCMRING2:18</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_1_16_8_1_1_2"><span class="kw">case </span></a><a NAME="E1:36_1_16_8_1_1_2"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c17">da</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">R</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c1">k</font>,<span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K1" title="SCMNORM:func.1">succ</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:36_1_16_8_1_1_2"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c1">k</font>,<span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K1" title="SCMNORM:func.1">succ</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:36_1"><span class="lab"><font color="Green" title="E33">A11</font></span></a>, <a class="txt" href="#E32:36_1"><span class="lab"><font color="Green" title="E57">A42</font></span></a>, <a class="txt" href="#E13:36_1"><span class="lab"><font color="Green" title="E43">A21</font></span></a>, <a class="txt" href="#E3:36_1_16_8"><span class="lab"><font color="Green" title="E68">A102</font></span></a>, <a class="ref" href="scmring2.html#T18" title="SCMRING2:th.18">SCMRING2:18</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div><a NAME="E5:36_1_16_8"/><span class="lab"><font color="Green" title="E70">A104</font></span>: 
 <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">da</font> <a href="scmring2.html#K10" title="SCMRING2:func.10">=0_goto</a> <span class="p1">(<span class="default"><font color="Maroon" title="c18">loc</font> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c1">k</font>,<span class="p2">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:36_1"><span class="lab"><font color="Green" title="E34">A12</font></span></a>, <a class="txt" href="#E3:36_1_16_8"><span class="lab"><font color="Green" title="E68">A102</font></span></a>, <a class="ref" href="scmring3.html#T70" title="SCMRING3:th.70">SCMRING3:70</a></span>;<br/><div><span class="lab"><font color="Green" title="E71">A105</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="36_1_16_8_2"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_1_16_8_2_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:36_1_16_8_2_1"/>
( <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c17">da</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">R</font> or <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c17">da</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">R</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_1_16_8_2_1_1"><span class="kw">case </span></a><a NAME="E1:36_1_16_8_2_1_1"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c17">da</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">R</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">loc</font> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c1">k</font>,<span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:36_1_16_8_2_1_1"/>
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">loc</font> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c1">k</font>,<span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:36_1"><span class="lab"><font color="Green" title="E38">A15</font></span></a>, <a class="txt" href="#E5:36_1_16_8"><span class="lab"><font color="Green" title="E70">A104</font></span></a>, <a class="ref" href="scmring2.html#T18" title="SCMRING2:th.18">SCMRING2:18</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_1_16_8_2_1_2"><span class="kw">case </span></a><a NAME="E1:36_1_16_8_2_1_2"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c17">da</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">R</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K1" title="SCMNORM:func.1">succ</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:36_1_16_8_2_1_2"/>
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K1" title="SCMNORM:func.1">succ</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:36_1"><span class="lab"><font color="Green" title="E38">A15</font></span></a>, <a class="txt" href="#E5:36_1_16_8"><span class="lab"><font color="Green" title="E70">A104</font></span></a>, <a class="ref" href="scmring2.html#T18" title="SCMRING2:th.18">SCMRING2:18</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div><a NAME="E7:36_1_16_8"/><span class="lab"><font color="Green" title="E72">A106</font></span>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c17">da</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c17">da</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:36_1"><span class="lab"><font color="Green" title="E40">A17</font></span></a></span>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="36_1_16_8_3"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_1_16_8_3_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:36_1_16_8_3_1"/>
( <font color="Maroon" title="c18">loc</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="scmnorm.html#K1" title="SCMNORM:func.1">succ</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span> or <font color="Maroon" title="c18">loc</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K1" title="SCMNORM:func.1">succ</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_1_16_8_3_1_1"><span class="kw">suppose </span></a><a NAME="E1:36_1_16_8_3_1_1"/>
<font color="Maroon" title="c18">loc</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="scmnorm.html#K1" title="SCMNORM:func.1">succ</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c1">k</font>,<span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:36_1_16_8_3_1_1"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c1">k</font>,<span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:36"><span class="lab"><font color="Green" title="E23">A1</font></span></a>, <a class="txt" href="#E3:36"><span class="lab"><font color="Green" title="E25">A3</font></span></a>, <a class="txt" href="#E6:36"><span class="lab"><font color="Green" title="E28">A6</font></span></a>, <a class="txt" href="#E10:36"><span class="lab"><font color="Green" title="E31">A9</font></span></a>, <a class="txt" href="#E3:36_1_16_8"><span class="lab"><font color="Green" title="E68">A102</font></span></a>, <a class="txt" href="#E7:36_1_16_8"><span class="lab"><font color="Green" title="E72">A106</font></span></a>, <a class="txt" href="#E4:36_1_16_8"><span class="lab"><font color="Green" title="E69">A103</font></span></a>, <a class="txt" href="#E6:36_1_16_8"><span class="lab"><font color="Green" title="E71">A105</font></span></a>, <a class="ref" href="scmring4.html#T33" target="_self" title="SCMRING4:th.33">Th33</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_1_16_8_3_1_2"><span class="kw">suppose </span></a><a NAME="E1:36_1_16_8_3_1_2"/>
<font color="Maroon" title="c18">loc</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K1" title="SCMNORM:func.1">succ</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c1">k</font>,<span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:36_1_16_8_3_1_2"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c1">k</font>,<span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:36_1"><span class="lab"><font color="Green" title="E33">A11</font></span></a>, <a class="txt" href="#E13:36_1"><span class="lab"><font color="Green" title="E43">A21</font></span></a>, <a class="txt" href="#E4:36_1_16_8"><span class="lab"><font color="Green" title="E69">A103</font></span></a>, <a class="txt" href="#E6:36_1_16_8"><span class="lab"><font color="Green" title="E71">A105</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E9:36_1_16_8"/>
( <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c1">k</font>,<span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> &amp;  <a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:36_1"><span class="lab"><font color="Green" title="E44">A22</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c1">k</font></span>)</span></span>)</span></span>)</span> &amp;  <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> )</span><br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="36_1_16_8_4"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c19">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">x</font> )</span><br/><span class="kw">assume </span><a NAME="E1:36_1_16_8_4"/><span class="lab"><font color="Green" title="E73">A107</font></span>: 
<font color="Maroon" title="c19">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">x</font></span><br/><a NAME="E2:36_1_16_8_4"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmring4.html#T13" target="_self" title="SCMRING4:th.13">Th13</a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c20">d</font> = <font color="Maroon" title="c19">x</font> as    <a href="scmring2.html#M1" title="SCMRING2:mode.1">Data-Location</a> of <font color="Maroon" title="c2">R</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E34:36_1"><span class="lab"><font color="Green" title="E59">A44</font></span></a>, <a class="txt" href="#E1:36_1_16_8_4"><span class="lab"><font color="Green" title="E73">A107</font></span></a>, <a class="ref" href="scmring2.html#T1" title="SCMRING2:th.1">SCMRING2:1</a></span>;<br/><a NAME="E4:36_1_16_8_4"/>
( <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c20">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c20">d</font> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c20">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c20">d</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E32:36_1"><span class="lab"><font color="Green" title="E57">A42</font></span></a>, <a class="txt" href="#E6:36_1"><span class="lab"><font color="Green" title="E38">A15</font></span></a>, <a class="txt" href="#E3:36_1_16_8"><span class="lab"><font color="Green" title="E68">A102</font></span></a>, <a class="txt" href="#E5:36_1_16_8"><span class="lab"><font color="Green" title="E70">A104</font></span></a>, <a class="ref" href="scmring2.html#T18" title="SCMRING2:th.18">SCMRING2:18</a></span>;<br/><span class="kw">hence </span><a NAME="E5:36_1_16_8_4"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E34:36_1"><span class="lab"><font color="Green" title="E59">A44</font></span></a>, <a class="txt" href="#E39:36_1"><span class="lab"><font color="Green" title="E64">A49</font></span></a>, <a class="txt" href="#E1:36_1_16_8_4"><span class="lab"><font color="Green" title="E73">A107</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><a NAME="E11:36_1_16_8"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E37:36_1"><span class="lab"><font color="Green" title="E62">A47</font></span></a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></span>;<br/><span class="kw">hence </span><a NAME="E12:36_1_16_8"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c1">k</font></span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E35:36_1"><span class="lab"><font color="Green" title="E60">A45</font></span></a>, <a class="txt" href="#E34:36_1"><span class="lab"><font color="Green" title="E59">A44</font></span></a>, <a class="txt" href="#E36:36_1"><span class="lab"><font color="Green" title="E61">A46</font></span></a>, <a class="ref" href="grfunc_1.html#T9" title="GRFUNC_1:th.9">GRFUNC_1:9</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span><br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="36_1_16_8_5"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c19">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> implies <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">x</font> )</span><br/><span class="kw">assume </span><a NAME="E1:36_1_16_8_5"/><span class="lab"><font color="Green" title="E73">A108</font></span>: 
<font color="Maroon" title="c19">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">x</font></span><br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c20">d</font> = <font color="Maroon" title="c19">x</font> as    <a href="scmring2.html#M1" title="SCMRING2:mode.1">Data-Location</a> of <font color="Maroon" title="c2">R</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:36_1"><span class="lab"><font color="Green" title="E48">A30</font></span></a>, <a class="ref" href="scmring2.html#T1" title="SCMRING2:th.1">SCMRING2:1</a></span>;<br/><a NAME="E3:36_1_16_8_5"/>
( <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c20">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c20">d</font> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c20">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Maroon" title="c8">i</font></span>)</span> <a href="scmring2.html#K3" title="SCMRING2:func.3">.</a> <font color="Maroon" title="c20">d</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:36_1"><span class="lab"><font color="Green" title="E38">A15</font></span></a>, <a class="txt" href="#E42:36_1"><span class="lab"><font color="Green" title="E67">A57</font></span></a>, <a class="txt" href="#E3:36_1_16_8"><span class="lab"><font color="Green" title="E68">A102</font></span></a>, <a class="txt" href="#E5:36_1_16_8"><span class="lab"><font color="Green" title="E70">A104</font></span></a>, <a class="ref" href="scmring2.html#T18" title="SCMRING2:th.18">SCMRING2:18</a></span>;<br/><span class="kw">hence </span><a NAME="E4:36_1_16_8_5"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E26:36_1"><span class="lab"><font color="Green" title="E53">A37</font></span></a>, <a class="txt" href="#E1:36_1_16_8_5"><span class="lab"><font color="Green" title="E73">A108</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><a NAME="E14:36_1_16_8"/><span class="kw">then </span>
 <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:36_1"><span class="lab"><font color="Green" title="E49">A31</font></span></a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></span>;<br/><span class="kw">hence </span><a NAME="E15:36_1_16_8"/>
 <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:36_1"><span class="lab"><font color="Green" title="E48">A30</font></span></a>, <a class="txt" href="#E23:36_1"><span class="lab"><font color="Green" title="E50">A32</font></span></a>, <a class="ref" href="grfunc_1.html#T9" title="GRFUNC_1:th.9">GRFUNC_1:9</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

</div><span class="kw">end;</span></div>
<a NAME="E12:36"/><span class="lab"><font color="Green" title="E33">Y</font></span>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c3">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">s1</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c3">s1</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#T150" title="AMI_1:th.150">AMI_1:150</a></span>;<br/>
<a NAME="E13:36"/>
 <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">s1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#T13" title="AMI_1:th.13">AMI_1:13</a></span>;<br/>
<span class="kw">then </span><span class="lab"><font color="Green" title="E34">A109</font></span>:  <a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span>,<font color="Maroon" title="c1">k</font> = 
 <a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c1">k</font>

<br/>.= 
 <a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s1</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <span class="p2">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c3">s1</font></span>)</span></span>)</span>,<font color="Maroon" title="c1">k</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:36"><span class="lab"><font color="Green" title="E33">Y</font></span></a></span>
;<br/>
<a NAME="E15:36"/><span class="lab"><font color="Green" title="E35">A110</font></span>: 
 <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c1">k</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c1">k</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T88" title="RELAT_1:th.88">RELAT_1:88</a></span>;<br/>
<a NAME="E16:36"/><span class="lab"><font color="Green" title="E36">A111</font></span>: 
 <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">p</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T88" title="RELAT_1:th.88">RELAT_1:88</a></span>;<br/>
<a NAME="E17:36"/><span class="lab"><font color="Green" title="E37">A112</font></span>: 
 <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c1">k</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="amistd_2.html#T68" title="AMISTD_2:th.68">AMISTD_2:68</a></span>;<br/>
<span class="lab"><font color="Green" title="E38">A113</font></span>: <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span> = 
<font color="Maroon" title="c3">s1</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#T13" title="AMI_1:th.13">AMI_1:13</a></span>
<br/>.= 
 <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:36"><span class="lab"><font color="Green" title="E25">A3</font></span></a>, <a class="txt" href="#E16:36"><span class="lab"><font color="Green" title="E36">A111</font></span></a>, <a class="ref" href="grfunc_1.html#T64" title="GRFUNC_1:th.64">GRFUNC_1:64</a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></span>
<br/>.= 
<font color="Maroon" title="c4">s2</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:36"><span class="lab"><font color="Green" title="E26">A4</font></span></a>, <a class="txt" href="#E17:36"><span class="lab"><font color="Green" title="E37">A112</font></span></a>, <a class="txt" href="#E15:36"><span class="lab"><font color="Green" title="E35">A110</font></span></a>, <a class="ref" href="grfunc_1.html#T64" title="GRFUNC_1:th.64">GRFUNC_1:64</a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c1">k</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:36"><span class="lab"><font color="Green" title="E37">A112</font></span></a>, <a class="ref" href="ami_1.html#T13" title="AMI_1:th.13">AMI_1:13</a></span>
;<br/>
<span class="lab"><font color="Green" title="E39">A114</font></span>:  <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> = 
 <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c4">s2</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:36"><span class="lab"><font color="Green" title="E27">A5</font></span></a>, <a class="ref" href="ami_1.html#T13" title="AMI_1:th.13">AMI_1:13</a></span>
<br/>.= 
 <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c4">s2</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="pboole.html#T157" title="PBOOLE:th.157">PBOOLE:157</a></span>
<br/>.= 
 <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#T13" title="AMI_1:th.13">AMI_1:13</a></span>
;<br/>
<a NAME="E20:36"/><span class="lab"><font color="Green" title="E40">A115</font></span>: 
 <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c1">k</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="amistd_2.html#T72" title="AMISTD_2:th.72">AMISTD_2:72</a></span>;<br/>
<span class="lab"><font color="Green" title="E41">A116</font></span>: <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c1">k</font>,<span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c3">s1</font></span>)</span> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c1">k</font>,<span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#T13" title="AMI_1:th.13">AMI_1:13</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c6">p</font></span>)</span> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c1">k</font>,<span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:36"><span class="lab"><font color="Green" title="E24">A2</font></span></a>, <a class="txt" href="#E3:36"><span class="lab"><font color="Green" title="E25">A3</font></span></a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></span>
<br/>.= 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c1">k</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="amistd_2.html#T73" title="AMISTD_2:th.73">AMISTD_2:73</a></span>
<br/>.= 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c4">s2</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:36"><span class="lab"><font color="Green" title="E26">A4</font></span></a>, <a class="txt" href="#E20:36"><span class="lab"><font color="Green" title="E40">A115</font></span></a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></span>
<br/>.= 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#T13" title="AMI_1:th.13">AMI_1:13</a></span>
;<br/>
<a NAME="E22:36"/><span class="lab"><font color="Green" title="E42">A117</font></span>: 
 <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c1">k</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="amistd_2.html#T72" title="AMISTD_2:th.72">AMISTD_2:72</a></span>;<br/>
<a NAME="E23:36"/>
 <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c6">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">p</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T88" title="RELAT_1:th.88">RELAT_1:88</a></span>;<br/>
<a NAME="E24:36"/><span class="kw">then </span><span class="lab"><font color="Green" title="E43">A118</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c6">p</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c6">p</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></span>;<br/>
<a NAME="E25:36"/><span class="kw">then </span><span class="lab"><font color="Green" title="E44">A119</font></span>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c6">p</font></span>)</span> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c1">k</font>,<span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c1">k</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:36"><span class="lab"><font color="Green" title="E30">A8</font></span></a>, <a class="ref" href="amistd_2.html#T71" title="AMISTD_2:th.71">AMISTD_2:71</a></span>;<br/>
<a NAME="E26:36"/><span class="lab"><font color="Green" title="E45">Y</font></span>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c1">k</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">s2</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c1">k</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#T150" title="AMI_1:th.150">AMI_1:150</a></span>;<br/>
<a NAME="E27:36"/>
 <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">s2</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#T13" title="AMI_1:th.13">AMI_1:13</a></span>;<br/>
<span class="kw">then </span><span class="lab"><font color="Green" title="E46">A120</font></span>:  <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> = 
 <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>

<br/>.= 
<font color="Maroon" title="c4">s2</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c1">k</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:36"><span class="lab"><font color="Green" title="E26">A4</font></span></a>, <a class="txt" href="#E22:36"><span class="lab"><font color="Green" title="E42">A117</font></span></a>, <a class="txt" href="#E26:36"><span class="lab"><font color="Green" title="E45">Y</font></span></a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></span>
<br/>.= 
<font color="Maroon" title="c4">s2</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c6">p</font></span>)</span> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c1">k</font>,<span class="p2">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="amistd_2.html#T73" title="AMISTD_2:th.73">AMISTD_2:73</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c1">k</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c6">p</font></span>)</span> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c1">k</font>,<span class="p2">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:36"><span class="lab"><font color="Green" title="E26">A4</font></span></a>, <a class="txt" href="#E25:36"><span class="lab"><font color="Green" title="E44">A119</font></span></a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></span>
;<br/>
<a NAME="E29:36"/>
<font color="Maroon" title="c6">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c6">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">s1</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c3">s1</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:36"><span class="lab"><font color="Green" title="E25">A3</font></span></a>, <a class="txt" href="#E7:36"><span class="lab"><font color="Green" title="E29">A7</font></span></a>, <a class="txt" href="#E9:36"><span class="lab"><font color="Green" title="E30">A8</font></span></a>, <a class="txt" href="#E24:36"><span class="lab"><font color="Green" title="E43">A118</font></span></a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></span>;<br/>
<a NAME="E30:36"/><span class="kw">then </span><span class="lab"><font color="Green" title="E47">A121</font></span>: 
<font color="Maroon">S<sub>1</sub></font>[ <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ]
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:36"><span class="lab"><font color="Green" title="E41">A116</font></span></a>, <a class="txt" href="#E9:36"><span class="lab"><font color="Green" title="E30">A8</font></span></a>, <a class="txt" href="#E14:36"><span class="lab"><font color="Green" title="E34">A109</font></span></a>, <a class="txt" href="#E28:36"><span class="lab"><font color="Green" title="E46">A120</font></span></a>, <a class="txt" href="#E18:36"><span class="lab"><font color="Green" title="E38">A113</font></span></a>, <a class="txt" href="#E19:36"><span class="lab"><font color="Green" title="E39">A114</font></span></a>, <a class="ref" href="amistd_2.html#T76" title="AMISTD_2:th.76">AMISTD_2:76</a></span>;<br/>
<a NAME="E31:36"/>
for <font color="Olive" title="b1">n</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>  holds  <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">n</font>]
 
<span class="kw">from</span> <span class="lab"><a class="ref" href="nat_1.html#S1" title="NAT_1:sch.1">NAT_1:sch 1</a>(<a class="txt" href="#E30:36"><span class="lab"><font color="Green" title="E47">A121</font></span></a>, <a class="txt" href="#E11:36"><span class="lab"><font color="Green" title="E32">A10</font></span></a>);<br/></span>
<span class="kw">hence </span><a NAME="E32:36"/>
for <font color="Olive" title="b1">i</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>  holds <br/> ( <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Olive" title="b1">i</font></span>)</span></span>)</span> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c1">k</font>,<span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Olive" title="b1">i</font></span>)</span> &amp;  <a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Olive" title="b1">i</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Olive" title="b1">i</font></span>)</span></span>)</span>,<font color="Maroon" title="c1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Olive" title="b1">i</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Olive" title="b1">i</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Olive" title="b1">i</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Olive" title="b1">i</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c1">k</font></span>)</span></span>)</span></span>)</span> &amp;  <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c5">s</font></span>)</span>,<font color="Maroon" title="c5">s</font>,<font color="Olive" title="b1">i</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Olive" title="b1">i</font></span>)</span> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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