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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">p</font> being  <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 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="b3">F</font> being  <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <span class="p1">(<span class="default"><a href="ami_1.html#K14" title="AMI_1:func.14">FinPartSt</a> <span class="p2">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Olive" title="b1">R</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="ami_1.html#K14" title="AMI_1:func.14">FinPartSt</a> <span class="p2">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Olive" title="b1">R</font></span>)</span></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="b2">p</font> &amp; <font color="Olive" title="b3">F</font> is  <a href="ami_1.html#V15" title="AMI_1:attr.15">data-only</a>  holds <br/>(  <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Olive" title="b2">p</font>,<font color="Olive" title="b2">p</font> <a href="ami_1.html#R2" title="AMI_1:pred.2">computes</a> <font color="Olive" title="b3">F</font> iff  <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Olive" title="b2">p</font>,<font color="Maroon" title="c1">k</font></span>)</span>, <a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Olive" title="b2">p</font>,<font color="Maroon" title="c1">k</font> <a href="ami_1.html#R2" title="AMI_1:pred.2">computes</a> <font color="Olive" title="b3">F</font> )</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">p</font> being  <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 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="b2">F</font> being  <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <span class="p1">(<span class="default"><a href="ami_1.html#K14" title="AMI_1:func.14">FinPartSt</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>,<span class="p1">(<span class="default"><a href="ami_1.html#K14" title="AMI_1:func.14">FinPartSt</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>  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="b2">F</font> is  <a href="ami_1.html#V15" title="AMI_1:attr.15">data-only</a>  holds <br/>(  <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Olive" title="b1">p</font>,<font color="Olive" title="b1">p</font> <a href="ami_1.html#R2" title="AMI_1:pred.2">computes</a> <font color="Olive" title="b2">F</font> iff  <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p1">(<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>, <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="ami_1.html#R2" title="AMI_1:pred.2">computes</a> <font color="Olive" title="b2">F</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c3">p</font> be   <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"> ( 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">F</font> being  <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <span class="p1">(<span class="default"><a href="ami_1.html#K14" title="AMI_1:func.14">FinPartSt</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>,<span class="p1">(<span class="default"><a href="ami_1.html#K14" title="AMI_1:func.14">FinPartSt</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>  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="Maroon" title="c3">p</font> &amp; <font color="Olive" title="b1">F</font> is  <a href="ami_1.html#V15" title="AMI_1:attr.15">data-only</a>  holds <br/>(  <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c3">p</font> <a href="ami_1.html#R2" title="AMI_1:pred.2">computes</a> <font color="Olive" title="b1">F</font> iff  <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c1">k</font></span>)</span>, <a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c1">k</font> <a href="ami_1.html#R2" title="AMI_1:pred.2">computes</a> <font color="Olive" title="b1">F</font> ) )</span><br/>





<span class="kw">assume </span><a NAME="E1:43"/><span class="lab"><font color="Green" title="E28">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">F</font> being  <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <span class="p1">(<span class="default"><a href="ami_1.html#K14" title="AMI_1:func.14">FinPartSt</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>,<span class="p1">(<span class="default"><a href="ami_1.html#K14" title="AMI_1:func.14">FinPartSt</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>  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="Maroon" title="c3">p</font> &amp; <font color="Olive" title="b1">F</font> is  <a href="ami_1.html#V15" title="AMI_1:attr.15">data-only</a>  holds <br/>(  <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c3">p</font> <a href="ami_1.html#R2" title="AMI_1:pred.2">computes</a> <font color="Olive" title="b1">F</font> iff  <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c1">k</font></span>)</span>, <a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c1">k</font> <a href="ami_1.html#R2" title="AMI_1:pred.2">computes</a> <font color="Olive" title="b1">F</font> )</span><br/>

<span class="kw">let </span><font color="Maroon" title="c4">F</font> be   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <span class="p1">(<span class="default"><a href="ami_1.html#K14" title="AMI_1:func.14">FinPartSt</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>,<span class="p1">(<span class="default"><a href="ami_1.html#K14" title="AMI_1:func.14">FinPartSt</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 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="c3">p</font> &amp; <font color="Maroon" title="c4">F</font> is  <a href="ami_1.html#V15" title="AMI_1:attr.15">data-only</a>  implies (  <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c3">p</font> <a href="ami_1.html#R2" title="AMI_1:pred.2">computes</a> <font color="Maroon" title="c4">F</font> iff  <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c1">k</font></span>)</span>, <a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c1">k</font> <a href="ami_1.html#R2" title="AMI_1:pred.2">computes</a> <font color="Maroon" title="c4">F</font> ) )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E2:43"/><span class="lab"><font color="Green" title="E29">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="c3">p</font>
 <span class="kw">and </span><br/><a NAME="E3:43"/><span class="lab"><font color="Green" title="E30">A3</font></span>: 
<font color="Maroon" title="c4">F</font> is  <a href="ami_1.html#V15" title="AMI_1:attr.15">data-only</a> 
 ; <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#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c3">p</font> <a href="ami_1.html#R2" title="AMI_1:pred.2">computes</a> <font color="Maroon" title="c4">F</font> iff  <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c1">k</font></span>)</span>, <a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c1">k</font> <a href="ami_1.html#R2" title="AMI_1:pred.2">computes</a> <font color="Maroon" title="c4">F</font> )</span><br/>

<a NAME="E4:43"/><span class="lab"><font color="Green" title="E31">F1</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">p</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c3">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">p</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T119" title="FUNCT_4:th.119">FUNCT_4:119</a></span>;<br/>
<a NAME="E5:43"/><span class="lab"><font color="Green" title="E32">F2</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="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c1">k</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c1">k</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c1">k</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T119" title="FUNCT_4:th.119">FUNCT_4:119</a></span>;<br/>
<div><span class="kw">hereby </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#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c1">k</font></span>)</span>, <a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c1">k</font> <a href="ami_1.html#R2" title="AMI_1:pred.2">computes</a> <font color="Maroon" title="c4">F</font> implies  <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c3">p</font> <a href="ami_1.html#R2" title="AMI_1:pred.2">computes</a> <font color="Maroon" title="c4">F</font> )</span>
<div class="add"><span class="kw">assume </span><a NAME="E1:43_1"/><span class="lab"><font color="Green" title="E33">A4</font></span>: 
 <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c3">p</font> <a href="ami_1.html#R2" title="AMI_1:pred.2">computes</a> <font color="Maroon" title="c4">F</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#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c1">k</font></span>)</span>, <a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c1">k</font> <a href="ami_1.html#R2" title="AMI_1:pred.2">computes</a> <font color="Maroon" title="c4">F</font></span><br/><span class="kw">thus </span><a NAME="E2:43_1"/>
 <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c1">k</font></span>)</span>, <a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c1">k</font> <a href="ami_1.html#R2" title="AMI_1:pred.2">computes</a> <font color="Maroon" title="c4">F</font>
  <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="43_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c5">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="ami_1.html#D30" title="AMI_1:def.30">AMI_1:def 30</a> <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="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">proj1</a> <font color="Maroon" title="c4">F</font> or  ex <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <br/>( <font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive">b<sub>1</sub></font> &amp; <span class="p1">(<span class="default"><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="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c1">k</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c1">k</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Olive">b<sub>1</sub></font> is    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  &amp; <font color="Maroon" title="c4">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="ami_1.html#K19" title="AMI_1:func.19">Result</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="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c1">k</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c1">k</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Olive">b<sub>1</sub></font></span>)</span> ) )</span><br/>

<span class="kw">assume </span><a NAME="E1:43_1_1"/><span class="lab"><font color="Green" title="E34">A5</font></span>: 
<font color="Maroon" title="c5">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> <font color="Maroon" title="c4">F</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <br/>( <font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive">b<sub>1</sub></font> &amp; <span class="p1">(<span class="default"><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="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c1">k</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c1">k</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Olive">b<sub>1</sub></font> is    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  &amp; <font color="Maroon" title="c4">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="ami_1.html#K19" title="AMI_1:func.19">Result</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="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c1">k</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c1">k</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Olive">b<sub>1</sub></font></span>)</span> )</span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c6">d1</font> being   <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><span class="kw"> such that </span><br/><a NAME="E3:43_1_1"/><span class="lab"><font color="Green" title="E35">A6</font></span>: 
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d1</font>
 <span class="kw">and </span><br/><a NAME="E4:43_1_1"/><span class="lab"><font color="Green" title="E36">A7</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">d1</font> is   <a href="ami_1.html#NM6" title="AMI_1:NM.6">pre-program</a> of  <a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font>
 <span class="kw">and </span><br/><a NAME="E5:43_1_1"/><span class="lab"><font color="Green" title="E37">A8</font></span>: 
<font color="Maroon" title="c4">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">d1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="ami_1.html#K19" title="AMI_1:func.19">Result</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">p</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">d1</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:43_1"><span class="lab"><font color="Green" title="E33">A4</font></span></a>, <a class="ref" href="ami_1.html#D30" title="AMI_1:def.30">AMI_1:def 30</a></span>;<br/>
<a NAME="E6:43_1_1"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c4">F</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="ami_1.html#K14" title="AMI_1:func.14">FinPartSt</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="relat_1.html#D18" title="RELAT_1:def.18">RELAT_1:def 18</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c7">d</font> = <font color="Maroon" title="c5">x</font> as   <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> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:43_1_1"><span class="lab"><font color="Green" title="E34">A5</font></span></a>, <a class="ref" href="ami_1.html#T125" title="AMI_1:th.125">AMI_1:125</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c8">d</font> = <font color="Maroon" title="c7">d</font> as   <a href="ami_1.html#V14" title="AMI_1:attr.14">data-only</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> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:43"><span class="lab"><font color="Green" title="E30">A3</font></span></a>, <a class="txt" href="#E1:43_1_1"><span class="lab"><font color="Green" title="E34">A5</font></span></a>, <a class="ref" href="ami_1.html#D52" title="AMI_1:def.52">AMI_1:def 52</a></span>;<br/>
<a NAME="E9:43_1_1"/><span class="lab"><font color="Green" title="E38">X</font></span>: 
 <a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">d</font></span>)</span>,<font color="Maroon" title="c1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c1">k</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">d</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:43"><span class="lab"><font color="Green" title="E29">A2</font></span></a>, <a class="ref" href="amistd_2.html#T78" title="AMISTD_2:th.78">AMISTD_2:78</a></span>;<br/>
<a NAME="E10:43_1_1"/><span class="lab"><font color="Green" title="E39">xx</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c8">d</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</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="ami_1.html#T155" title="AMI_1:th.155">AMI_1:155</a></span>;<br/>
<a NAME="E11:43_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E40">x</font></span>: 
 <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">d</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">p</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T76" title="FUNCT_4:th.76">FUNCT_4:76</a></span>;<br/>
<a NAME="E12:43_1_1"/><span class="lab"><font color="Green" title="E41">y</font></span>: 
 <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c1">k</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">d</font></span>)</span> <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="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c1">k</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:43_1_1"><span class="lab"><font color="Green" title="E39">xx</font></span></a>, <a class="ref" href="funct_4.html#T76" title="FUNCT_4:th.76">FUNCT_4:76</a></span>;<br/>
<a NAME="E13:43_1_1"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">d</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="c3">p</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c8">d</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#D1" title="FUNCT_4:def.1">FUNCT_4:def 1</a></span>;<br/>
<a NAME="E14:43_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E42">A9</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"><font color="Maroon" title="c3">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">d</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:43"><span class="lab"><font color="Green" title="E29">A2</font></span></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>;<br/>
<span class="kw">then </span><span class="lab"><font color="Green" title="E43">A10</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#K19" title="AMI_1:func.19">Result</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">p</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">d1</font></span>)</span></span>)</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#K19" title="AMI_1:func.19">Result</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="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c1">k</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">d</font></span>)</span>,<font color="Maroon" title="c1">k</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:43"><span class="lab"><font color="Green" title="E28">A1</font></span></a>, <a class="txt" href="#E3:43_1_1"><span class="lab"><font color="Green" title="E35">A6</font></span></a>, <a class="txt" href="#E4:43_1_1"><span class="lab"><font color="Green" title="E36">A7</font></span></a>, <a class="ref" href="scmring4.html#T41" target="_self" title="SCMRING4:th.41">Th41</a>, <a class="txt" href="#E4:43"><span class="lab"><font color="Green" title="E31">F1</font></span></a>, <a class="txt" href="#E11:43_1_1"><span class="lab"><font color="Green" title="E40">x</font></span></a>, <a class="txt" href="#E9:43_1_1"><span class="lab"><font color="Green" title="E38">X</font></span></a>, <a class="txt" href="#E12:43_1_1"><span class="lab"><font color="Green" title="E41">y</font></span></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#K19" title="AMI_1:func.19">Result</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="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c1">k</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c1">k</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">d</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:43_1_1"><span class="lab"><font color="Green" title="E38">X</font></span></a></span>
;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c9">Fd1</font> = <font color="Maroon" title="c4">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">d1</font> as   <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> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:43_1_1"><span class="lab"><font color="Green" title="E37">A8</font></span></a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c8">d</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="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">d</font> &amp; <span class="p1">(<span class="default"><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="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c1">k</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c1">k</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">d</font> is    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  &amp; <font color="Maroon" title="c4">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">d</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="ami_1.html#K19" title="AMI_1:func.19">Result</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="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c1">k</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c1">k</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">d</font></span>)</span> )</span><br/>

<span class="kw">thus </span><a NAME="E17:43_1_1"/>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">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#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c1">k</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c1">k</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">d</font> is    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  &amp; <font color="Maroon" title="c4">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">d</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="ami_1.html#K19" title="AMI_1:func.19">Result</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="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c1">k</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c1">k</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">d</font></span>)</span> )</span><br/>

<a NAME="E18:43_1_1"/>
<span class="p1">(<span class="default"><a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c1">k</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">d</font></span>)</span>,<font color="Maroon" title="c1">k</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:43"><span class="lab"><font color="Green" title="E29">A2</font></span></a>, <a class="ref" href="amistd_2.html#T78" title="AMISTD_2:th.78">AMISTD_2:78</a></span>;<br/>
<span class="kw">hence </span><a NAME="E19:43_1_1"/>
<span class="p1">(<span class="default"><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="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c1">k</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c1">k</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">d</font> is   <a href="ami_1.html#NM6" title="AMI_1:NM.6">pre-program</a> of  <a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:43"><span class="lab"><font color="Green" title="E28">A1</font></span></a>, <a class="txt" href="#E3:43_1_1"><span class="lab"><font color="Green" title="E35">A6</font></span></a>, <a class="txt" href="#E4:43_1_1"><span class="lab"><font color="Green" title="E36">A7</font></span></a>, <a class="txt" href="#E14:43_1_1"><span class="lab"><font color="Green" title="E42">A9</font></span></a>, <a class="ref" href="scmring4.html#T36" target="_self" title="SCMRING4:th.36">Th36</a>, <a class="txt" href="#E4:43"><span class="lab"><font color="Green" title="E31">F1</font></span></a>, <a class="txt" href="#E5:43"><span class="lab"><font color="Green" title="E32">F2</font></span></a>, <a class="ref" href="scmring4.html#T40" target="_self" title="SCMRING4:th.40">Th40</a></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" title="c4">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">d</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="ami_1.html#K19" title="AMI_1:func.19">Result</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="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c1">k</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c1">k</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">d</font></span>)</span></span><br/>

<a NAME="E20:43_1_1"/><span class="lab"><font color="Green" title="E44">A11</font></span>: 
<font color="Maroon" title="c9">Fd1</font> is  <a href="ami_1.html#V14" title="AMI_1:attr.14">data-only</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:43"><span class="lab"><font color="Green" title="E30">A3</font></span></a>, <a class="txt" href="#E1:43_1_1"><span class="lab"><font color="Green" title="E34">A5</font></span></a>, <a class="txt" href="#E3:43_1_1"><span class="lab"><font color="Green" title="E35">A6</font></span></a>, <a class="ref" href="ami_1.html#D52" title="AMI_1:def.52">AMI_1:def 52</a></span>;<br/>
<a NAME="E21:43_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c4">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">d1</font> <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#K19" title="AMI_1:func.19">Result</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">p</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">d1</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:43_1_1"><span class="lab"><font color="Green" title="E37">A8</font></span></a>, <a class="ref" href="ami_1.html#T107" title="AMI_1:th.107">AMI_1:107</a></span>;<br/>
<span class="kw">hence </span><a NAME="E22:43_1_1"/>
<font color="Maroon" title="c4">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">d</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="ami_1.html#K19" title="AMI_1:func.19">Result</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="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c1">k</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c1">k</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">d</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:43_1_1"><span class="lab"><font color="Green" title="E35">A6</font></span></a>, <a class="txt" href="#E20:43_1_1"><span class="lab"><font color="Green" title="E44">A11</font></span></a>, <a class="txt" href="#E15:43_1_1"><span class="lab"><font color="Green" title="E43">A10</font></span></a>, <a class="ref" href="ami_1.html#T107" title="AMI_1:th.107">AMI_1:107</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>

<span class="kw">assume </span><a NAME="E7:43"/><span class="lab"><font color="Green" title="E33">A12</font></span>: 
 <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c1">k</font></span>)</span>, <a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c1">k</font> <a href="ami_1.html#R2" title="AMI_1:pred.2">computes</a> <font color="Maroon" title="c4">F</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#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c3">p</font> <a href="ami_1.html#R2" title="AMI_1:pred.2">computes</a> <font color="Maroon" title="c4">F</font></span><br/>

<span class="kw">let </span><font color="Maroon" title="c5">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="ami_1.html#D30" title="AMI_1:def.30">AMI_1:def 30</a> <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="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">proj1</a> <font color="Maroon" title="c4">F</font> or  ex <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <br/>( <font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive">b<sub>1</sub></font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Olive">b<sub>1</sub></font> is    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  &amp; <font color="Maroon" title="c4">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="ami_1.html#K19" title="AMI_1:func.19">Result</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">p</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Olive">b<sub>1</sub></font></span>)</span> ) )</span><br/>

<span class="kw">assume </span><a NAME="E8:43"/><span class="lab"><font color="Green" title="E34">A13</font></span>: 
<font color="Maroon" title="c5">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> <font color="Maroon" title="c4">F</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <br/>( <font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive">b<sub>1</sub></font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Olive">b<sub>1</sub></font> is    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  &amp; <font color="Maroon" title="c4">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="ami_1.html#K19" title="AMI_1:func.19">Result</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">p</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Olive">b<sub>1</sub></font></span>)</span> )</span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c6">d1</font> being   <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><span class="kw"> such that </span><br/><a NAME="E10:43"/><span class="lab"><font color="Green" title="E35">A14</font></span>: 
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d1</font>
 <span class="kw">and </span><br/><a NAME="E11:43"/><span class="lab"><font color="Green" title="E36">A15</font></span>: 
<span class="p1">(<span class="default"><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="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c1">k</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c1">k</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">d1</font> is   <a href="ami_1.html#NM6" title="AMI_1:NM.6">pre-program</a> of  <a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font>
 <span class="kw">and </span><br/><a NAME="E12:43"/><span class="lab"><font color="Green" title="E37">A16</font></span>: 
<font color="Maroon" title="c4">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">d1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="ami_1.html#K19" title="AMI_1:func.19">Result</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="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c1">k</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c1">k</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">d1</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:43"><span class="lab"><font color="Green" title="E33">A12</font></span></a>, <a class="ref" href="ami_1.html#D30" title="AMI_1:def.30">AMI_1:def 30</a></span>;<br/>
<a NAME="E13:43"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c4">F</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="ami_1.html#K14" title="AMI_1:func.14">FinPartSt</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="relat_1.html#D18" title="RELAT_1:def.18">RELAT_1:def 18</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c7">d</font> = <font color="Maroon" title="c5">x</font> as   <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> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:43"><span class="lab"><font color="Green" title="E34">A13</font></span></a>, <a class="ref" href="ami_1.html#T125" title="AMI_1:th.125">AMI_1:125</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c8">d</font> = <font color="Maroon" title="c7">d</font> as   <a href="ami_1.html#V14" title="AMI_1:attr.14">data-only</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> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:43"><span class="lab"><font color="Green" title="E30">A3</font></span></a>, <a class="txt" href="#E8:43"><span class="lab"><font color="Green" title="E34">A13</font></span></a>, <a class="ref" href="ami_1.html#D52" title="AMI_1:def.52">AMI_1:def 52</a></span>;<br/>
<a NAME="E16:43"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">d</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="c3">p</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c8">d</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#D1" title="FUNCT_4:def.1">FUNCT_4:def 1</a></span>;<br/>
<a NAME="E17:43"/><span class="kw">then </span><span class="lab"><font color="Green" title="E38">A17</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"><font color="Maroon" title="c3">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">d</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:43"><span class="lab"><font color="Green" title="E29">A2</font></span></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>;<br/>
<a NAME="E18:43"/><span class="lab"><font color="Green" title="E39">A18</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="c3">p</font>,<font color="Maroon" title="c1">k</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">d</font></span>)</span>,<font color="Maroon" title="c1">k</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:43"><span class="lab"><font color="Green" title="E29">A2</font></span></a>, <a class="ref" href="amistd_2.html#T78" title="AMISTD_2:th.78">AMISTD_2:78</a></span>;<br/>
<a NAME="E19:43"/><span class="kw">then </span><span class="lab"><font color="Green" title="E40">A19</font></span>: 
<font color="Maroon" title="c3">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">d</font> is  <a href="ami_1.html#V10" title="AMI_1:attr.10">autonomic</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:43"><span class="lab"><font color="Green" title="E28">A1</font></span></a>, <a class="txt" href="#E10:43"><span class="lab"><font color="Green" title="E35">A14</font></span></a>, <a class="txt" href="#E11:43"><span class="lab"><font color="Green" title="E36">A15</font></span></a>, <a class="txt" href="#E17:43"><span class="lab"><font color="Green" title="E38">A17</font></span></a>, <a class="ref" href="scmring4.html#T40" target="_self" title="SCMRING4:th.40">Th40</a>, <a class="txt" href="#E5:43"><span class="lab"><font color="Green" title="E32">F2</font></span></a></span>;<br/>
<a NAME="E20:43"/><span class="kw">then </span><span class="lab"><font color="Green" title="E41">A20</font></span>: 
<font color="Maroon" title="c3">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">d</font> is  <a href="ami_1.html#V11" title="AMI_1:attr.11">halting</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:43"><span class="lab"><font color="Green" title="E28">A1</font></span></a>, <a class="txt" href="#E10:43"><span class="lab"><font color="Green" title="E35">A14</font></span></a>, <a class="txt" href="#E11:43"><span class="lab"><font color="Green" title="E36">A15</font></span></a>, <a class="txt" href="#E18:43"><span class="lab"><font color="Green" title="E39">A18</font></span></a>, <a class="txt" href="#E17:43"><span class="lab"><font color="Green" title="E38">A17</font></span></a>, <a class="ref" href="scmring4.html#T36" target="_self" title="SCMRING4:th.36">Th36</a>, <a class="txt" href="#E5:43"><span class="lab"><font color="Green" title="E32">F2</font></span></a></span>;<br/>
<a NAME="E21:43"/><span class="lab"><font color="Green" title="E42">X</font></span>: 
 <a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">d</font></span>)</span>,<font color="Maroon" title="c1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c1">k</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">d</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:43"><span class="lab"><font color="Green" title="E29">A2</font></span></a>, <a class="ref" href="amistd_2.html#T78" title="AMISTD_2:th.78">AMISTD_2:78</a></span>;<br/>
<a NAME="E22:43"/><span class="lab"><font color="Green" title="E43">xx</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c8">d</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</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="ami_1.html#T155" title="AMI_1:th.155">AMI_1:155</a></span>;<br/>
<a NAME="E23:43"/><span class="kw">then </span><span class="lab"><font color="Green" title="E44">x</font></span>: 
 <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">d</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">p</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T76" title="FUNCT_4:th.76">FUNCT_4:76</a></span>;<br/>
<a NAME="E24:43"/><span class="lab"><font color="Green" title="E45">y</font></span>: 
 <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c1">k</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">d</font></span>)</span> <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="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c1">k</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:43"><span class="lab"><font color="Green" title="E43">xx</font></span></a>, <a class="ref" href="funct_4.html#T76" title="FUNCT_4:th.76">FUNCT_4:76</a></span>;<br/>
<span class="lab"><font color="Green" title="E46">A21</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#K19" title="AMI_1:func.19">Result</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="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c1">k</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c1">k</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">d1</font></span>)</span></span>)</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#K19" title="AMI_1:func.19">Result</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="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c1">k</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">d</font></span>)</span>,<font color="Maroon" title="c1">k</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:43"><span class="lab"><font color="Green" title="E35">A14</font></span></a>, <a class="txt" href="#E21:43"><span class="lab"><font color="Green" title="E42">X</font></span></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#K19" title="AMI_1:func.19">Result</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">p</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">d</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:43"><span class="lab"><font color="Green" title="E28">A1</font></span></a>, <a class="txt" href="#E17:43"><span class="lab"><font color="Green" title="E38">A17</font></span></a>, <a class="txt" href="#E19:43"><span class="lab"><font color="Green" title="E40">A19</font></span></a>, <a class="txt" href="#E20:43"><span class="lab"><font color="Green" title="E41">A20</font></span></a>, <a class="ref" href="scmring4.html#T41" target="_self" title="SCMRING4:th.41">Th41</a>, <a class="txt" href="#E23:43"><span class="lab"><font color="Green" title="E44">x</font></span></a>, <a class="txt" href="#E24:43"><span class="lab"><font color="Green" title="E45">y</font></span></a>, <a class="txt" href="#E21:43"><span class="lab"><font color="Green" title="E42">X</font></span></a></span>
;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c8">d</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="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">d</font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">d</font> is    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  &amp; <font color="Maroon" title="c4">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">d</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="ami_1.html#K19" title="AMI_1:func.19">Result</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">p</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">d</font></span>)</span> )</span><br/>

<span class="kw">thus </span><a NAME="E26:43"/>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">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#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">d</font> is    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  &amp; <font color="Maroon" title="c4">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">d</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="ami_1.html#K19" title="AMI_1:func.19">Result</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">p</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">d</font></span>)</span> )</span><br/>

<span class="kw">thus </span><a NAME="E27:43"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">d</font> is   <a href="ami_1.html#NM6" title="AMI_1:NM.6">pre-program</a> of  <a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:43"><span class="lab"><font color="Green" title="E28">A1</font></span></a>, <a class="txt" href="#E10:43"><span class="lab"><font color="Green" title="E35">A14</font></span></a>, <a class="txt" href="#E11:43"><span class="lab"><font color="Green" title="E36">A15</font></span></a>, <a class="txt" href="#E18:43"><span class="lab"><font color="Green" title="E39">A18</font></span></a>, <a class="txt" href="#E17:43"><span class="lab"><font color="Green" title="E38">A17</font></span></a>, <a class="txt" href="#E19:43"><span class="lab"><font color="Green" title="E40">A19</font></span></a>, <a class="ref" href="scmring4.html#T36" target="_self" title="SCMRING4:th.36">Th36</a>, <a class="txt" href="#E4:43"><span class="lab"><font color="Green" title="E31">F1</font></span></a>, <a class="txt" href="#E5:43"><span class="lab"><font color="Green" title="E32">F2</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"> <font color="Maroon" title="c4">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">d</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="ami_1.html#K19" title="AMI_1:func.19">Result</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">p</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">d</font></span>)</span></span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c9">Fd1</font> = <font color="Maroon" title="c4">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">d1</font> as   <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> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:43"><span class="lab"><font color="Green" title="E37">A16</font></span></a></span>;<br/>
<a NAME="E29:43"/><span class="lab"><font color="Green" title="E47">A22</font></span>: 
<font color="Maroon" title="c9">Fd1</font> is  <a href="ami_1.html#V14" title="AMI_1:attr.14">data-only</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:43"><span class="lab"><font color="Green" title="E30">A3</font></span></a>, <a class="txt" href="#E8:43"><span class="lab"><font color="Green" title="E34">A13</font></span></a>, <a class="txt" href="#E10:43"><span class="lab"><font color="Green" title="E35">A14</font></span></a>, <a class="ref" href="ami_1.html#D52" title="AMI_1:def.52">AMI_1:def 52</a></span>;<br/>
<a NAME="E30:43"/><span class="kw">then </span>
<font color="Maroon" title="c4">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">d1</font> <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#K19" title="AMI_1:func.19">Result</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="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c1">k</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="amistd_2.html#K13" title="AMISTD_2:func.13">Relocated</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c1">k</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">d1</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:43"><span class="lab"><font color="Green" title="E37">A16</font></span></a>, <a class="ref" href="ami_1.html#T107" title="AMI_1:th.107">AMI_1:107</a></span>;<br/>
<span class="kw">hence </span><a NAME="E31:43"/>
<font color="Maroon" title="c4">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">d</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="ami_1.html#K19" title="AMI_1:func.19">Result</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">p</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">d</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:43"><span class="lab"><font color="Green" title="E35">A14</font></span></a>, <a class="txt" href="#E29:43"><span class="lab"><font color="Green" title="E47">A22</font></span></a>, <a class="txt" href="#E25:43"><span class="lab"><font color="Green" title="E46">A21</font></span></a>, <a class="ref" href="ami_1.html#T107" title="AMI_1:th.107">AMI_1:107</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/>


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