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<span class="kw">let </span><font color="Maroon" title="c1">p</font> be  non  <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>   <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 ; <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> being  <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>   st <font color="Maroon" title="c1">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">s1</font> &amp; <font color="Maroon" title="c1">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">s2</font> holds <br/>for <font color="Olive" title="b3">i</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> <br/> for <font color="Olive" title="b4">da</font>, <font color="Olive" title="b5">db</font> being   <a href="ami_3.html#M1" title="AMI_3:mode.1">Data-Location</a> <br/> for <font color="Olive" title="b6">I</font> being  <a href="ami_1.html#NM2" title="AMI_1:NM.2">Instruction</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>   st <font color="Olive" title="b6">I</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> <font color="Olive" title="b1">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="Olive" title="b1">s1</font></span>)</span>,<font color="Olive" title="b1">s1</font>,<font color="Olive" title="b3">i</font></span>)</span> &amp; <font color="Olive" title="b6">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K5" title="AMI_3:func.5">SubFrom</a> <font color="Olive" title="b4">da</font>,<font color="Olive" title="b5">db</font> &amp; <font color="Olive" title="b4">da</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> <font color="Maroon" title="c1">p</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="Olive" title="b1">s1</font></span>)</span>,<font color="Olive" title="b1">s1</font>,<font color="Olive" title="b3">i</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Olive" title="b4">da</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_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="Olive" title="b1">s1</font></span>)</span>,<font color="Olive" title="b1">s1</font>,<font color="Olive" title="b3">i</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Olive" title="b5">db</font></span>)</span> <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="Olive" title="b2">s2</font></span>)</span>,<font color="Olive" title="b2">s2</font>,<font color="Olive" title="b3">i</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Olive" title="b4">da</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_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="Olive" title="b2">s2</font></span>)</span>,<font color="Olive" title="b2">s2</font>,<font color="Olive" title="b3">i</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Olive" title="b5">db</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">s1</font>, <font color="Maroon" title="c3">s2</font> be   <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</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="c1">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">s1</font> &amp; <font color="Maroon" title="c1">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">s2</font> implies for <font color="Olive" title="b1">i</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> <br/> for <font color="Olive" title="b2">da</font>, <font color="Olive" title="b3">db</font> being   <a href="ami_3.html#M1" title="AMI_3:mode.1">Data-Location</a> <br/> for <font color="Olive" title="b4">I</font> being  <a href="ami_1.html#NM2" title="AMI_1:NM.2">Instruction</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>   st <font color="Olive" title="b4">I</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> <font color="Maroon" title="c2">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="c2">s1</font></span>)</span>,<font color="Maroon" title="c2">s1</font>,<font color="Olive" title="b1">i</font></span>)</span> &amp; <font color="Olive" title="b4">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K5" title="AMI_3:func.5">SubFrom</a> <font color="Olive" title="b2">da</font>,<font color="Olive" title="b3">db</font> &amp; <font color="Olive" title="b2">da</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> <font color="Maroon" title="c1">p</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="c2">s1</font></span>)</span>,<font color="Maroon" title="c2">s1</font>,<font color="Olive" title="b1">i</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Olive" title="b2">da</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_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="c2">s1</font></span>)</span>,<font color="Maroon" title="c2">s1</font>,<font color="Olive" title="b1">i</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Olive" title="b3">db</font></span>)</span> <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">s2</font></span>)</span>,<font color="Maroon" title="c3">s2</font>,<font color="Olive" title="b1">i</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Olive" title="b2">da</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_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">s2</font></span>)</span>,<font color="Maroon" title="c3">s2</font>,<font color="Olive" title="b1">i</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Olive" title="b3">db</font></span>)</span> )</span><br/>



<span class="kw">assume </span><a NAME="E1:89"/><span class="lab"><font color="Green" title="E21">A1</font></span>: 
( <font color="Maroon" title="c1">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">s1</font> &amp; <font color="Maroon" title="c1">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">s2</font> )
 ; <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#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> <br/> for <font color="Olive" title="b2">da</font>, <font color="Olive" title="b3">db</font> being   <a href="ami_3.html#M1" title="AMI_3:mode.1">Data-Location</a> <br/> for <font color="Olive" title="b4">I</font> being  <a href="ami_1.html#NM2" title="AMI_1:NM.2">Instruction</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>   st <font color="Olive" title="b4">I</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> <font color="Maroon" title="c2">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="c2">s1</font></span>)</span>,<font color="Maroon" title="c2">s1</font>,<font color="Olive" title="b1">i</font></span>)</span> &amp; <font color="Olive" title="b4">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K5" title="AMI_3:func.5">SubFrom</a> <font color="Olive" title="b2">da</font>,<font color="Olive" title="b3">db</font> &amp; <font color="Olive" title="b2">da</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> <font color="Maroon" title="c1">p</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="c2">s1</font></span>)</span>,<font color="Maroon" title="c2">s1</font>,<font color="Olive" title="b1">i</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Olive" title="b2">da</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_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="c2">s1</font></span>)</span>,<font color="Maroon" title="c2">s1</font>,<font color="Olive" title="b1">i</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Olive" title="b3">db</font></span>)</span> <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">s2</font></span>)</span>,<font color="Maroon" title="c3">s2</font>,<font color="Olive" title="b1">i</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Olive" title="b2">da</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_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">s2</font></span>)</span>,<font color="Maroon" title="c3">s2</font>,<font color="Olive" title="b1">i</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Olive" title="b3">db</font></span>)</span></span><br/>

<span class="kw">let </span><font color="Maroon" title="c4">i</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">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"> for <font color="Olive" title="b1">da</font>, <font color="Olive" title="b2">db</font> being   <a href="ami_3.html#M1" title="AMI_3:mode.1">Data-Location</a> <br/> for <font color="Olive" title="b3">I</font> being  <a href="ami_1.html#NM2" title="AMI_1:NM.2">Instruction</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>   st <font color="Olive" title="b3">I</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> <font color="Maroon" title="c2">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="c2">s1</font></span>)</span>,<font color="Maroon" title="c2">s1</font>,<font color="Maroon" title="c4">i</font></span>)</span> &amp; <font color="Olive" title="b3">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K5" title="AMI_3:func.5">SubFrom</a> <font color="Olive" title="b1">da</font>,<font color="Olive" title="b2">db</font> &amp; <font color="Olive" title="b1">da</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> <font color="Maroon" title="c1">p</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="c2">s1</font></span>)</span>,<font color="Maroon" title="c2">s1</font>,<font color="Maroon" title="c4">i</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Olive" title="b1">da</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_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="c2">s1</font></span>)</span>,<font color="Maroon" title="c2">s1</font>,<font color="Maroon" title="c4">i</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Olive" title="b2">db</font></span>)</span> <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">s2</font></span>)</span>,<font color="Maroon" title="c3">s2</font>,<font color="Maroon" title="c4">i</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Olive" title="b1">da</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_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">s2</font></span>)</span>,<font color="Maroon" title="c3">s2</font>,<font color="Maroon" title="c4">i</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Olive" title="b2">db</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c5">da</font>, <font color="Maroon" title="c6">db</font> be    <a href="ami_3.html#M1" title="AMI_3:mode.1">Data-Location</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">I</font> being  <a href="ami_1.html#NM2" title="AMI_1:NM.2">Instruction</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>   st <font color="Olive" title="b1">I</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> <font color="Maroon" title="c2">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="c2">s1</font></span>)</span>,<font color="Maroon" title="c2">s1</font>,<font color="Maroon" title="c4">i</font></span>)</span> &amp; <font color="Olive" title="b1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K5" title="AMI_3:func.5">SubFrom</a> <font color="Maroon" title="c5">da</font>,<font color="Maroon" title="c6">db</font> &amp; <font color="Maroon" title="c5">da</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> <font color="Maroon" title="c1">p</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="c2">s1</font></span>)</span>,<font color="Maroon" title="c2">s1</font>,<font color="Maroon" title="c4">i</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c5">da</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_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="c2">s1</font></span>)</span>,<font color="Maroon" title="c2">s1</font>,<font color="Maroon" title="c4">i</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c6">db</font></span>)</span> <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">s2</font></span>)</span>,<font color="Maroon" title="c3">s2</font>,<font color="Maroon" title="c4">i</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c5">da</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_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">s2</font></span>)</span>,<font color="Maroon" title="c3">s2</font>,<font color="Maroon" title="c4">i</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c6">db</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c7">I</font> be   <a href="ami_1.html#NM2" title="AMI_1:NM.2">Instruction</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</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="c7">I</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> <font color="Maroon" title="c2">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="c2">s1</font></span>)</span>,<font color="Maroon" title="c2">s1</font>,<font color="Maroon" title="c4">i</font></span>)</span> &amp; <font color="Maroon" title="c7">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K5" title="AMI_3:func.5">SubFrom</a> <font color="Maroon" title="c5">da</font>,<font color="Maroon" title="c6">db</font> &amp; <font color="Maroon" title="c5">da</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> <font color="Maroon" title="c1">p</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="c2">s1</font></span>)</span>,<font color="Maroon" title="c2">s1</font>,<font color="Maroon" title="c4">i</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c5">da</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_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="c2">s1</font></span>)</span>,<font color="Maroon" title="c2">s1</font>,<font color="Maroon" title="c4">i</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c6">db</font></span>)</span> <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">s2</font></span>)</span>,<font color="Maroon" title="c3">s2</font>,<font color="Maroon" title="c4">i</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c5">da</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_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">s2</font></span>)</span>,<font color="Maroon" title="c3">s2</font>,<font color="Maroon" title="c4">i</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c6">db</font></span>)</span> )</span><br/>





<span class="kw">assume </span><a NAME="E2:89"/><span class="lab"><font color="Green" title="E22">A2</font></span>: 
<font color="Maroon" title="c7">I</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> <font color="Maroon" title="c2">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="c2">s1</font></span>)</span>,<font color="Maroon" title="c2">s1</font>,<font color="Maroon" title="c4">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"> (  not <font color="Maroon" title="c7">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K5" title="AMI_3:func.5">SubFrom</a> <font color="Maroon" title="c5">da</font>,<font color="Maroon" title="c6">db</font> or  not <font color="Maroon" title="c5">da</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> <font color="Maroon" title="c1">p</font> or <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="c2">s1</font></span>)</span>,<font color="Maroon" title="c2">s1</font>,<font color="Maroon" title="c4">i</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c5">da</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_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="c2">s1</font></span>)</span>,<font color="Maroon" title="c2">s1</font>,<font color="Maroon" title="c4">i</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c6">db</font></span>)</span> <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">s2</font></span>)</span>,<font color="Maroon" title="c3">s2</font>,<font color="Maroon" title="c4">i</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c5">da</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_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">s2</font></span>)</span>,<font color="Maroon" title="c3">s2</font>,<font color="Maroon" title="c4">i</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c6">db</font></span>)</span> )</span><br/>

<span class="kw">set </span><font color="Maroon" title="c8">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="c3">s2</font></span>)</span>,<font color="Maroon" title="c3">s2</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">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="c9">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="c3">s2</font></span>)</span>,<font color="Maroon" title="c3">s2</font>,<font color="Maroon" title="c4">i</font>;<br/>
<a NAME="E3:89"/><span class="lab"><font color="Green" title="E23">T</font></span>: 
 <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">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="c3">s2</font></span>)</span>,<font color="Maroon" title="c3">s2</font>,<font color="Maroon" title="c4">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="E24">A3</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">s2</font></span>)</span>,<font color="Maroon" title="c3">s2</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">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">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="c3">s2</font></span>)</span>,<font color="Maroon" title="c3">s2</font>,<font color="Maroon" title="c4">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">s2</font></span>)</span>,<font color="Maroon" title="c3">s2</font>,<font color="Maroon" title="c4">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">s2</font></span>)</span>,<font color="Maroon" title="c3">s2</font>,<font color="Maroon" title="c4">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">s2</font></span>)</span>,<font color="Maroon" title="c3">s2</font>,<font color="Maroon" title="c4">i</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:89"><span class="lab"><font color="Green" title="E23">T</font></span></a></span>
;<br/>
<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E5:89"/><span class="lab"><font color="Green" title="E25">A4</font></span>: 
<font color="Maroon" title="c7">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K5" title="AMI_3:func.5">SubFrom</a> <font color="Maroon" title="c5">da</font>,<font color="Maroon" title="c6">db</font>
 <span class="kw">and </span><br/><a NAME="E6:89"/><span class="lab"><font color="Green" title="E26">A5</font></span>: 
( <font color="Maroon" title="c5">da</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> <font color="Maroon" title="c1">p</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="c2">s1</font></span>)</span>,<font color="Maroon" title="c2">s1</font>,<font color="Maroon" title="c4">i</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c5">da</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_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="c2">s1</font></span>)</span>,<font color="Maroon" title="c2">s1</font>,<font color="Maroon" title="c4">i</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c6">db</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</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">s2</font></span>)</span>,<font color="Maroon" title="c3">s2</font>,<font color="Maroon" title="c4">i</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c5">da</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_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">s2</font></span>)</span>,<font color="Maroon" title="c3">s2</font>,<font color="Maroon" title="c4">i</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c6">db</font></span>)</span> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E7:89"/><span class="lab"><font color="Green" title="E27">TY</font></span>: 
 <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">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="c3">s2</font></span>)</span>,<font color="Maroon" title="c3">s2</font>,<font color="Maroon" title="c4">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/>
<a NAME="E8:89"/>
<font color="Maroon" title="c7">I</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> <font color="Maroon" title="c3">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="c3">s2</font></span>)</span>,<font color="Maroon" title="c3">s2</font>,<font color="Maroon" title="c4">i</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:89"><span class="lab"><font color="Green" title="E21">A1</font></span></a>, <a class="txt" href="#E2:89"><span class="lab"><font color="Green" title="E22">A2</font></span></a>, <a class="ref" href="ami_5.html#T87" target="_self" title="AMI_5:th.87">Th87</a></span>;<br/>
<a NAME="E9:89"/><span class="kw">then </span><span class="lab"><font color="Green" title="E28">A6</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">s2</font></span>)</span>,<font color="Maroon" title="c3">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c5">da</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">s2</font></span>)</span>,<font color="Maroon" title="c3">s2</font>,<font color="Maroon" title="c4">i</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c5">da</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_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">s2</font></span>)</span>,<font color="Maroon" title="c3">s2</font>,<font color="Maroon" title="c4">i</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c6">db</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:89"><span class="lab"><font color="Green" title="E24">A3</font></span></a>, <a class="txt" href="#E5:89"><span class="lab"><font color="Green" title="E25">A4</font></span></a>, <a class="txt" href="#E7:89"><span class="lab"><font color="Green" title="E27">TY</font></span></a>, <a class="ref" href="ami_3.html#T10" title="AMI_3:th.10">AMI_3:10</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c10">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="c2">s1</font></span>)</span>,<font color="Maroon" title="c2">s1</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">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="c11">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="c2">s1</font></span>)</span>,<font color="Maroon" title="c2">s1</font>,<font color="Maroon" title="c4">i</font>;<br/>
<a NAME="E10:89"/><span class="lab"><font color="Green" title="E29">T</font></span>: 
 <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">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="c2">s1</font></span>)</span>,<font color="Maroon" title="c2">s1</font>,<font color="Maroon" title="c4">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/>
<a NAME="E11:89"/><span class="lab"><font color="Green" title="E30">A7</font></span>: 
( <font color="Maroon" title="c5">da</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> <font color="Maroon" title="c1">p</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="c2">s1</font></span>)</span>,<font color="Maroon" title="c2">s1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c4">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> <font color="Maroon" title="c1">p</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">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="c2">s1</font></span>)</span>,<font color="Maroon" title="c2">s1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c5">da</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="c3">s2</font></span>)</span>,<font color="Maroon" title="c3">s2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c4">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> <font color="Maroon" title="c1">p</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">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="c3">s2</font></span>)</span>,<font color="Maroon" title="c3">s2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c5">da</font> ) )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></span>;<br/>
<a NAME="E12:89"/><span class="lab"><font color="Green" title="E31">TX</font></span>: 
 <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">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="c2">s1</font></span>)</span>,<font color="Maroon" title="c2">s1</font>,<font color="Maroon" title="c4">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/>
 <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="c2">s1</font></span>)</span>,<font color="Maroon" title="c2">s1</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">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="c2">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="c2">s1</font></span>)</span>,<font color="Maroon" title="c2">s1</font>,<font color="Maroon" title="c4">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="c2">s1</font></span>)</span>,<font color="Maroon" title="c2">s1</font>,<font color="Maroon" title="c4">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="c2">s1</font></span>)</span>,<font color="Maroon" title="c2">s1</font>,<font color="Maroon" title="c4">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="c2">s1</font></span>)</span>,<font color="Maroon" title="c2">s1</font>,<font color="Maroon" title="c4">i</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:89"><span class="lab"><font color="Green" title="E29">T</font></span></a></span>
;<br/>
<a NAME="E14:89"/><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="c2">s1</font></span>)</span>,<font color="Maroon" title="c2">s1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c5">da</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="c2">s1</font></span>)</span>,<font color="Maroon" title="c2">s1</font>,<font color="Maroon" title="c4">i</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c5">da</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_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="c2">s1</font></span>)</span>,<font color="Maroon" title="c2">s1</font>,<font color="Maroon" title="c4">i</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c6">db</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:89"><span class="lab"><font color="Green" title="E22">A2</font></span></a>, <a class="txt" href="#E5:89"><span class="lab"><font color="Green" title="E25">A4</font></span></a>, <a class="txt" href="#E12:89"><span class="lab"><font color="Green" title="E31">TX</font></span></a>, <a class="ref" href="ami_3.html#T10" title="AMI_3:th.10">AMI_3:10</a></span>;<br/>
<span class="kw">hence </span><a NAME="E15:89"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:89"><span class="lab"><font color="Green" title="E21">A1</font></span></a>, <a class="txt" href="#E11:89"><span class="lab"><font color="Green" title="E30">A7</font></span></a>, <a class="txt" href="#E6:89"><span class="lab"><font color="Green" title="E26">A5</font></span></a>, <a class="txt" href="#E9:89"><span class="lab"><font color="Green" title="E28">A6</font></span></a>, <a class="ref" href="ami_1.html#D25" title="AMI_1:def.25">AMI_1:def 25</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>
