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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">s</font> being  <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</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">s</font> holds <br/>for <font color="Olive" title="b2">i</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>  holds   <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Olive" title="b1">s</font></span>)</span>,<font color="Olive" title="b1">s</font>,<font color="Olive" title="b2">i</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c1">p</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">s</font> be   <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</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">s</font> implies for <font color="Olive" title="b1">i</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>  holds   <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font>,<font color="Olive" title="b1">i</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c1">p</font></span>)</span> )</span><br/>



<span class="kw">assume </span><a NAME="E1:18"/><span class="lab"><font color="Green" title="E5">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">s</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#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>  holds   <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font>,<font color="Olive" title="b1">i</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c1">p</font></span>)</span></span><br/>

<span class="kw">let </span><font color="Maroon" title="c3">i</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font>,<font color="Maroon" title="c3">i</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c1">p</font></span>)</span></span><br/>

<span class="kw">set </span><font color="Maroon" title="c4">Csi</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">s</font></span>)</span>,<font color="Maroon" title="c2">s</font>,<font color="Maroon" title="c3">i</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c5">loc</font> =  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font>,<font color="Maroon" title="c3">i</font></span>)</span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c6">ll</font> =  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font>,<font color="Maroon" title="c3">i</font></span>)</span> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>  ;<br/>
<span class="kw">set </span><font color="Maroon" title="c7">loc1</font> = <font color="Maroon" title="c6">ll</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1;<br/>
<a NAME="E3:18"/><span class="lab"><font color="Green" title="E6">A3</font></span>: 
(  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font>,<font color="Maroon" title="c3">i</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c1">p</font></span>)</span> iff  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font>,<font color="Maroon" title="c3">i</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<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> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</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="relat_1.html#T90" title="RELAT_1:th.90">RELAT_1:90</a></span>;<br/>
<span class="kw">assume </span><a NAME="E4:18"/>
not  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font>,<font color="Maroon" title="c3">i</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c1">p</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="E5:18"/><span class="kw">then </span><span class="lab"><font color="Green" title="E7">A4</font></span>: 
not  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font>,<font color="Maroon" title="c3">i</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="c1">p</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:18"><span class="lab"><font color="Green" title="E6">A3</font></span></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c8">p2</font> = <font color="Maroon" title="c1">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <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">s</font></span>)</span>,<font color="Maroon" title="c2">s</font>,<font color="Maroon" title="c3">i</font></span>)</span></span>)</span> <a href="ami_1.html#K22" title="AMI_1:func.22">.--&gt;</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">goto</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">ll</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c9">p1</font> = <font color="Maroon" title="c1">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <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">s</font></span>)</span>,<font color="Maroon" title="c2">s</font>,<font color="Maroon" title="c3">i</font></span>)</span></span>)</span> <a href="ami_1.html#K22" title="AMI_1:func.22">.--&gt;</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">goto</a> <span class="p3">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p5">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font>,<font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span></span>)</span>;<br/>
<a NAME="E6:18"/><span class="lab"><font color="Green" title="E8">A5</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p5">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font>,<font color="Maroon" title="c3">i</font></span>)</span></span>)</span> <a href="ami_1.html#K22" title="AMI_1:func.22">.--&gt;</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">goto</a> <span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p0">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font>,<font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span></span>)</span></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="c1">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> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p5">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font>,<font color="Maroon" title="c3">i</font></span>)</span></span>)</span> <a href="ami_1.html#K22" title="AMI_1:func.22">.--&gt;</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">goto</a> <span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p0">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font>,<font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span></span>)</span></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="E7:18"/><span class="lab"><font color="Green" title="E9">A6</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font>,<font color="Maroon" title="c3">i</font></span>)</span></span>)</span> <a href="ami_1.html#K22" title="AMI_1:func.22">.--&gt;</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">goto</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">ll</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font>,<font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T19" title="FUNCOP_1:th.19">FUNCOP_1:19</a></span>;<br/>
<a NAME="E8:18"/><span class="kw">then </span><span class="lab"><font color="Green" title="E10">A7</font></span>: 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font>,<font color="Maroon" title="c3">i</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"><span class="p2">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font>,<font color="Maroon" title="c3">i</font></span>)</span></span>)</span> <a href="ami_1.html#K22" title="AMI_1:func.22">.--&gt;</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">goto</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">ll</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/>
<a NAME="E9:18"/><span class="lab"><font color="Green" title="E11">A8</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p5">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font>,<font color="Maroon" title="c3">i</font></span>)</span></span>)</span> <a href="ami_1.html#K22" title="AMI_1:func.22">.--&gt;</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">goto</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">ll</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></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="c1">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> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p5">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font>,<font color="Maroon" title="c3">i</font></span>)</span></span>)</span> <a href="ami_1.html#K22" title="AMI_1:func.22">.--&gt;</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">goto</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">ll</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></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="E10:18"/><span class="kw">then </span><span class="lab"><font color="Green" title="E12">A9</font></span>: 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font>,<font color="Maroon" title="c3">i</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="c1">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p5">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font>,<font color="Maroon" title="c3">i</font></span>)</span></span>)</span> <a href="ami_1.html#K22" title="AMI_1:func.22">.--&gt;</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">goto</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">ll</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:18"><span class="lab"><font color="Green" title="E10">A7</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">consider </span><font color="Maroon" title="c10">s2</font> being   <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> <span class="kw"> such that </span><br/><a NAME="E12:18"/><span class="lab"><font color="Green" title="E13">A10</font></span>: 
<font color="Maroon" title="c1">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <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">s</font></span>)</span>,<font color="Maroon" title="c2">s</font>,<font color="Maroon" title="c3">i</font></span>)</span></span>)</span> <a href="ami_1.html#K22" title="AMI_1:func.22">.--&gt;</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">goto</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">ll</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c10">s2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="pboole.html#T156" title="PBOOLE:th.156">PBOOLE:156</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c11">Cs2i</font> =  <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c10">s2</font></span>)</span>,<font color="Maroon" title="c10">s2</font>,<font color="Maroon" title="c3">i</font>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c12">s1</font> being   <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> <span class="kw"> such that </span><br/><a NAME="E14:18"/><span class="lab"><font color="Green" title="E14">A11</font></span>: 
<font color="Maroon" title="c1">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <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">s</font></span>)</span>,<font color="Maroon" title="c2">s</font>,<font color="Maroon" title="c3">i</font></span>)</span></span>)</span> <a href="ami_1.html#K22" title="AMI_1:func.22">.--&gt;</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">goto</a> <span class="p3">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p5">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font>,<font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c12">s1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="pboole.html#T156" title="PBOOLE:th.156">PBOOLE:156</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c13">Cs1i</font> =  <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c12">s1</font></span>)</span>,<font color="Maroon" title="c12">s1</font>,<font color="Maroon" title="c3">i</font>;<br/>
<a NAME="E15:18"/><span class="lab"><font color="Green" title="E15">A12</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font>,<font color="Maroon" title="c3">i</font></span>)</span></span>)</span> <a href="ami_1.html#K22" title="AMI_1:func.22">.--&gt;</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">goto</a> <span class="p3">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p5">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font>,<font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font>,<font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T19" title="FUNCOP_1:th.19">FUNCOP_1:19</a></span>;<br/>
<a NAME="E16:18"/><span class="kw">then </span><span class="lab"><font color="Green" title="E16">A13</font></span>: 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font>,<font color="Maroon" title="c3">i</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"><span class="p2">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font>,<font color="Maroon" title="c3">i</font></span>)</span></span>)</span> <a href="ami_1.html#K22" title="AMI_1:func.22">.--&gt;</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">goto</a> <span class="p3">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p5">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font>,<font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/>
<a NAME="E17:18"/><span class="kw">then </span><span class="lab"><font color="Green" title="E17">A14</font></span>: 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font>,<font color="Maroon" title="c3">i</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="c1">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p5">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font>,<font color="Maroon" title="c3">i</font></span>)</span></span>)</span> <a href="ami_1.html#K22" title="AMI_1:func.22">.--&gt;</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">goto</a> <span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p0">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font>,<font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:18"><span class="lab"><font color="Green" title="E8">A5</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="E18:18"/>
not <font color="Maroon" title="c1">p</font> is  <a href="ami_1.html#V10" title="AMI_1:attr.10">autonomic</a> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="18_1"><span class="kw">proof </span></a><div class="add">

<div><span class="lab"><font color="Green" title="E18">A15</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="18_1_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c14">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c14">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="c1">p</font> implies <font color="Maroon" title="c1">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">s2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">x</font> )</span><br/><span class="kw">assume </span><a NAME="E1:18_1_1"/><span class="lab"><font color="Green" title="E19">A16</font></span>: 
<font color="Maroon" title="c14">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="c1">p</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="c1">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">s2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">x</font></span><br/><a NAME="E2:18_1_1"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">p</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font>,<font color="Maroon" title="c3">i</font></span>)</span></span>)</span> <a href="ami_1.html#K22" title="AMI_1:func.22">.--&gt;</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">goto</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">ll</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:18"><span class="lab"><font color="Green" title="E7">A4</font></span></a>, <a class="txt" href="#E7:18"><span class="lab"><font color="Green" title="E9">A6</font></span></a>, <a class="ref" href="zfmisc_1.html#T56" title="ZFMISC_1:th.56">ZFMISC_1:56</a></span>;<br/><a NAME="E3:18_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E20">A17</font></span>: 
<font color="Maroon" title="c1">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p5">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font>,<font color="Maroon" title="c3">i</font></span>)</span></span>)</span> <a href="ami_1.html#K22" title="AMI_1:func.22">.--&gt;</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">goto</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">ll</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:18_1_1"><span class="lab"><font color="Green" title="E19">A16</font></span></a>, <a class="ref" href="funct_4.html#T17" title="FUNCT_4:th.17">FUNCT_4:17</a></span>;<br/><a NAME="E4:18_1_1"/>
<font color="Maroon" title="c14">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p5">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font>,<font color="Maroon" title="c3">i</font></span>)</span></span>)</span> <a href="ami_1.html#K22" title="AMI_1:func.22">.--&gt;</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">goto</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">ll</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:18"><span class="lab"><font color="Green" title="E11">A8</font></span></a>, <a class="txt" href="#E1:18_1_1"><span class="lab"><font color="Green" title="E19">A16</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">hence </span><a NAME="E5:18_1_1"/>
<font color="Maroon" title="c1">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">s2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:18"><span class="lab"><font color="Green" title="E13">A10</font></span></a>, <a class="txt" href="#E3:18_1_1"><span class="lab"><font color="Green" title="E20">A17</font></span></a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<a NAME="E2:18_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font>,<font color="Maroon" title="c3">i</font></span>)</span></span>)</span> <a href="ami_1.html#K22" title="AMI_1:func.22">.--&gt;</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">goto</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">ll</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font>,<font color="Maroon" title="c3">i</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">goto</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">ll</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T87" title="FUNCOP_1:th.87">FUNCOP_1:87</a></span>;<br/>
<a NAME="E3:18_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p5">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font>,<font color="Maroon" title="c3">i</font></span>)</span></span>)</span> <a href="ami_1.html#K22" title="AMI_1:func.22">.--&gt;</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">goto</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">ll</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font>,<font color="Maroon" title="c3">i</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">goto</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">ll</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:18"><span class="lab"><font color="Green" title="E10">A7</font></span></a>, <a class="ref" href="funct_4.html#T14" title="FUNCT_4:th.14">FUNCT_4:14</a></span>;<br/>
<a NAME="E4:18_1"/><span class="kw">then </span>
<font color="Maroon" title="c10">s2</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</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">s</font></span>)</span>,<font color="Maroon" title="c2">s</font>,<font color="Maroon" title="c3">i</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">goto</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">ll</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:18"><span class="lab"><font color="Green" title="E12">A9</font></span></a>, <a class="txt" href="#E12:18"><span class="lab"><font color="Green" title="E13">A10</font></span></a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></span>;<br/>
<a NAME="E5:18_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E19">A18</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="c10">s2</font></span>)</span>,<font color="Maroon" title="c10">s2</font>,<font color="Maroon" title="c3">i</font></span>)</span> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font>,<font color="Maroon" title="c3">i</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">goto</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">ll</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#T54" title="AMI_1:th.54">AMI_1:54</a></span>;<br/>
<a NAME="E6:18_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font>,<font color="Maroon" title="c3">i</font></span>)</span></span>)</span> <a href="ami_1.html#K22" title="AMI_1:func.22">.--&gt;</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">goto</a> <span class="p3">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p5">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font>,<font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font>,<font color="Maroon" title="c3">i</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">goto</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font>,<font color="Maroon" title="c3">i</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T87" title="FUNCOP_1:th.87">FUNCOP_1:87</a></span>;<br/>
<a NAME="E7:18_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p5">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font>,<font color="Maroon" title="c3">i</font></span>)</span></span>)</span> <a href="ami_1.html#K22" title="AMI_1:func.22">.--&gt;</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">goto</a> <span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p0">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font>,<font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font>,<font color="Maroon" title="c3">i</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">goto</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font>,<font color="Maroon" title="c3">i</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:18"><span class="lab"><font color="Green" title="E16">A13</font></span></a>, <a class="ref" href="funct_4.html#T14" title="FUNCT_4:th.14">FUNCT_4:14</a></span>;<br/>
<a NAME="E8:18_1"/><span class="kw">then </span>
<font color="Maroon" title="c12">s1</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</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">s</font></span>)</span>,<font color="Maroon" title="c2">s</font>,<font color="Maroon" title="c3">i</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">goto</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font>,<font color="Maroon" title="c3">i</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:18"><span class="lab"><font color="Green" title="E17">A14</font></span></a>, <a class="txt" href="#E14:18"><span class="lab"><font color="Green" title="E14">A11</font></span></a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></span>;<br/>
<a NAME="E9:18_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E20">A19</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="c12">s1</font></span>)</span>,<font color="Maroon" title="c12">s1</font>,<font color="Maroon" title="c3">i</font></span>)</span> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font>,<font color="Maroon" title="c3">i</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">goto</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font>,<font color="Maroon" title="c3">i</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#T54" title="AMI_1:th.54">AMI_1:54</a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c12">s1</font>
; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="ami_1.html#D25" title="AMI_1:def.25">AMI_1:def 25</a> <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="c1">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c12">s1</font> &amp; <font color="Maroon" title="c1">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive">b<sub>1</sub></font> &amp; not for <font color="Olive">b<sub>2</sub></font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  holds  <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c12">s1</font></span>)</span>,<font color="Maroon" title="c12">s1</font>,<font color="Olive">b<sub>2</sub></font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">proj1</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Olive">b<sub>1</sub></font></span>)</span>,<font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">proj1</a> <font color="Maroon" title="c1">p</font></span>)</span> )</span><br/>

<span class="kw">take </span>
<font color="Maroon" title="c10">s2</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="c1">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c12">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="c10">s2</font> &amp; not for <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  holds  <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c12">s1</font></span>)</span>,<font color="Maroon" title="c12">s1</font>,<font color="Olive">b<sub>1</sub></font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">proj1</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c10">s2</font></span>)</span>,<font color="Maroon" title="c10">s2</font>,<font color="Olive">b<sub>1</sub></font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">proj1</a> <font color="Maroon" title="c1">p</font></span>)</span> )</span><br/>

<div><span class="lab"><font color="Green" title="E21">A20</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="18_1_2"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c14">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c14">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="c1">p</font> implies <font color="Maroon" title="c1">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">s1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">x</font> )</span><br/><span class="kw">assume </span><a NAME="E1:18_1_2"/><span class="lab"><font color="Green" title="E22">A21</font></span>: 
<font color="Maroon" title="c14">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="c1">p</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="c1">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">s1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">x</font></span><br/><a NAME="E2:18_1_2"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">p</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p4">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font>,<font color="Maroon" title="c3">i</font></span>)</span></span>)</span> <a href="ami_1.html#K22" title="AMI_1:func.22">.--&gt;</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">goto</a> <span class="p3">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p5">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font>,<font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:18"><span class="lab"><font color="Green" title="E7">A4</font></span></a>, <a class="txt" href="#E15:18"><span class="lab"><font color="Green" title="E15">A12</font></span></a>, <a class="ref" href="zfmisc_1.html#T56" title="ZFMISC_1:th.56">ZFMISC_1:56</a></span>;<br/><a NAME="E3:18_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E23">A22</font></span>: 
<font color="Maroon" title="c1">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p5">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font>,<font color="Maroon" title="c3">i</font></span>)</span></span>)</span> <a href="ami_1.html#K22" title="AMI_1:func.22">.--&gt;</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">goto</a> <span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p0">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font>,<font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:18_1_2"><span class="lab"><font color="Green" title="E22">A21</font></span></a>, <a class="ref" href="funct_4.html#T17" title="FUNCT_4:th.17">FUNCT_4:17</a></span>;<br/><a NAME="E4:18_1_2"/>
<font color="Maroon" title="c14">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p5">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font>,<font color="Maroon" title="c3">i</font></span>)</span></span>)</span> <a href="ami_1.html#K22" title="AMI_1:func.22">.--&gt;</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">goto</a> <span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p0">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font>,<font color="Maroon" title="c3">i</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:18"><span class="lab"><font color="Green" title="E8">A5</font></span></a>, <a class="txt" href="#E1:18_1_2"><span class="lab"><font color="Green" title="E22">A21</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">hence </span><a NAME="E5:18_1_2"/>
<font color="Maroon" title="c1">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">s1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:18"><span class="lab"><font color="Green" title="E14">A11</font></span></a>, <a class="txt" href="#E3:18_1_2"><span class="lab"><font color="Green" title="E23">A22</font></span></a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<a NAME="E11:18_1"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c12">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="partfun1.html#D4" title="PARTFUN1:def.4">PARTFUN1:def 4</a></span>;<br/>
<a NAME="E12:18_1"/><span class="kw">then </span>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c12">s1</font>
 
<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">hence </span><a NAME="E13:18_1"/><span class="lab"><font color="Green" title="E22">A23</font></span>: 
<font color="Maroon" title="c1">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c12">s1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:18_1"><span class="lab"><font color="Green" title="E21">A20</font></span></a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</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="c1">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c10">s2</font> &amp; not for <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  holds  <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c12">s1</font></span>)</span>,<font color="Maroon" title="c12">s1</font>,<font color="Olive">b<sub>1</sub></font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">proj1</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c10">s2</font></span>)</span>,<font color="Maroon" title="c10">s2</font>,<font color="Olive">b<sub>1</sub></font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">proj1</a> <font color="Maroon" title="c1">p</font></span>)</span> )</span><br/>

<a NAME="E14:18_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E23">A24</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="c12">s1</font></span>)</span>,<font color="Maroon" title="c12">s1</font>,<font color="Maroon" title="c3">i</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font>,<font color="Maroon" title="c3">i</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">p</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:18"><span class="lab"><font color="Green" title="E5">A1</font></span></a>, <a class="ref" href="ami_1.html#D25" title="AMI_1:def.25">AMI_1:def 25</a></span>;<br/>
<a NAME="E15:18_1"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c10">s2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="partfun1.html#D4" title="PARTFUN1:def.4">PARTFUN1:def 4</a></span>;<br/>
<a NAME="E16:18_1"/><span class="kw">then </span>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c10">s2</font>
 
<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">hence </span><a NAME="E17:18_1"/>
<font color="Maroon" title="c1">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c10">s2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:18_1"><span class="lab"><font color="Green" title="E18">A15</font></span></a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> not for <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  holds  <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c12">s1</font></span>)</span>,<font color="Maroon" title="c12">s1</font>,<font color="Olive">b<sub>1</sub></font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">proj1</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c10">s2</font></span>)</span>,<font color="Maroon" title="c10">s2</font>,<font color="Olive">b<sub>1</sub></font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">proj1</a> <font color="Maroon" title="c1">p</font></span>)</span></span><br/>

<a NAME="E18:18_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E24">A25</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="c12">s1</font></span>)</span>,<font color="Maroon" title="c12">s1</font>,<font color="Maroon" title="c3">i</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c10">s2</font></span>)</span>,<font color="Maroon" title="c10">s2</font>,<font color="Maroon" title="c3">i</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">p</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:18_1"><span class="lab"><font color="Green" title="E22">A23</font></span></a>, <a class="ref" href="ami_1.html#D25" title="AMI_1:def.25">AMI_1:def 25</a></span>;<br/>
<span class="kw">take </span><font color="Maroon" title="c14">k</font> = <font color="Maroon" title="c3">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> not <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c12">s1</font></span>)</span>,<font color="Maroon" title="c12">s1</font>,<font color="Maroon" title="c14">k</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">proj1</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c10">s2</font></span>)</span>,<font color="Maroon" title="c10">s2</font>,<font color="Maroon" title="c14">k</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">proj1</a> <font color="Maroon" title="c1">p</font></span>)</span></span><br/>

<span class="kw">set </span><font color="Maroon" title="c15">Cs1k</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="c12">s1</font></span>)</span>,<font color="Maroon" title="c12">s1</font>,<font color="Maroon" title="c14">k</font>;<br/>
<a NAME="E19:18_1"/><span class="lab"><font color="Green" title="E25">T</font></span>: 
 <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c12">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="c12">s1</font></span>)</span>,<font color="Maroon" title="c12">s1</font>,<font color="Maroon" title="c3">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="E26">A26</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="c12">s1</font></span>)</span>,<font color="Maroon" title="c12">s1</font>,<font color="Maroon" title="c14">k</font> = 
 <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="c12">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="c12">s1</font></span>)</span>,<font color="Maroon" title="c12">s1</font>,<font color="Maroon" title="c3">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> <font color="Maroon" title="c12">s1</font></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="c12">s1</font></span>)</span>,<font color="Maroon" title="c12">s1</font>,<font color="Maroon" title="c3">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="c12">s1</font></span>)</span>,<font color="Maroon" title="c12">s1</font>,<font color="Maroon" title="c3">i</font></span>)</span>

;<br/>
<a NAME="E21:18_1"/><span class="lab"><font color="Green" title="E27">Y</font></span>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c12">s1</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c12">s1</font></span>)</span>,<font color="Maroon" title="c12">s1</font>,<font color="Maroon" title="c3">i</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c12">s1</font></span>)</span>,<font color="Maroon" title="c12">s1</font>,<font color="Maroon" title="c3">i</font></span>)</span> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c12">s1</font></span>)</span>,<font color="Maroon" title="c12">s1</font>,<font color="Maroon" title="c3">i</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:18_1"><span class="lab"><font color="Green" title="E25">T</font></span></a>, <a class="ref" href="ami_1.html#T150" title="AMI_1:th.150">AMI_1:150</a></span>;<br/>
<a NAME="E22:18_1"/><span class="lab"><font color="Green" title="E28">A27</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="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font>,<font color="Maroon" title="c3">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </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="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font>,<font color="Maroon" title="c3">i</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">p</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_3.html#T15" target="_self" title="SCMFSA_3:th.15">Th15</a>, <a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></span>;<br/>
<a NAME="E23:18_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c12">s1</font></span>)</span>,<font color="Maroon" title="c12">s1</font>,<font color="Maroon" title="c3">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font>,<font color="Maroon" title="c3">i</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:18_1"><span class="lab"><font color="Green" title="E23">A24</font></span></a>, <a class="ref" href="scmfsa_3.html#T15" target="_self" title="SCMFSA_3:th.15">Th15</a>, <a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></span>;<br/>
<a NAME="E24:18_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E29">A28</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="c12">s1</font></span>)</span>,<font color="Maroon" title="c12">s1</font>,<font color="Maroon" title="c14">k</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font>,<font color="Maroon" title="c3">i</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:18_1"><span class="lab"><font color="Green" title="E26">A26</font></span></a>, <a class="txt" href="#E9:18_1"><span class="lab"><font color="Green" title="E20">A19</font></span></a>, <a class="txt" href="#E21:18_1"><span class="lab"><font color="Green" title="E27">Y</font></span></a>, <a class="ref" href="scmfsa_2.html#T95" title="SCMFSA_2:th.95">SCMFSA_2:95</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c16">Cs2k</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="c10">s2</font></span>)</span>,<font color="Maroon" title="c10">s2</font>,<font color="Maroon" title="c14">k</font>;<br/>
<a NAME="E25:18_1"/><span class="lab"><font color="Green" title="E30">T</font></span>: 
 <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c10">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="c10">s2</font></span>)</span>,<font color="Maroon" title="c10">s2</font>,<font color="Maroon" title="c3">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="E31">A29</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="c10">s2</font></span>)</span>,<font color="Maroon" title="c10">s2</font>,<font color="Maroon" title="c14">k</font> = 
 <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="c10">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="c10">s2</font></span>)</span>,<font color="Maroon" title="c10">s2</font>,<font color="Maroon" title="c3">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> <font color="Maroon" title="c10">s2</font></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="c10">s2</font></span>)</span>,<font color="Maroon" title="c10">s2</font>,<font color="Maroon" title="c3">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="c10">s2</font></span>)</span>,<font color="Maroon" title="c10">s2</font>,<font color="Maroon" title="c3">i</font></span>)</span>

;<br/>
<a NAME="E27:18_1"/><span class="lab"><font color="Green" title="E32">Z</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="c10">s2</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c10">s2</font></span>)</span>,<font color="Maroon" title="c10">s2</font>,<font color="Maroon" title="c3">i</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c10">s2</font></span>)</span>,<font color="Maroon" title="c10">s2</font>,<font color="Maroon" title="c3">i</font></span>)</span> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c10">s2</font></span>)</span>,<font color="Maroon" title="c10">s2</font>,<font color="Maroon" title="c3">i</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E25:18_1"><span class="lab"><font color="Green" title="E30">T</font></span></a>, <a class="ref" href="ami_1.html#T150" title="AMI_1:th.150">AMI_1:150</a></span>;<br/>
<a NAME="E28:18_1"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c10">s2</font></span>)</span>,<font color="Maroon" title="c10">s2</font>,<font color="Maroon" title="c3">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c2">s</font></span>)</span>,<font color="Maroon" title="c2">s</font>,<font color="Maroon" title="c3">i</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:18_1"><span class="lab"><font color="Green" title="E23">A24</font></span></a>, <a class="txt" href="#E22:18_1"><span class="lab"><font color="Green" title="E28">A27</font></span></a>, <a class="txt" href="#E18:18_1"><span class="lab"><font color="Green" title="E24">A25</font></span></a>, <a class="ref" href="scmfsa_3.html#T15" target="_self" title="SCMFSA_3:th.15">Th15</a>, <a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></span>;<br/>
<a NAME="E29:18_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E33">A30</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="c10">s2</font></span>)</span>,<font color="Maroon" title="c10">s2</font>,<font color="Maroon" title="c14">k</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">ll</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E26:18_1"><span class="lab"><font color="Green" title="E31">A29</font></span></a>, <a class="txt" href="#E5:18_1"><span class="lab"><font color="Green" title="E19">A18</font></span></a>, <a class="txt" href="#E27:18_1"><span class="lab"><font color="Green" title="E32">Z</font></span></a>, <a class="ref" href="scmfsa_2.html#T95" title="SCMFSA_2:th.95">SCMFSA_2:95</a></span>;<br/>
<a NAME="E30:18_1"/>
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c12">s1</font></span>)</span>,<font color="Maroon" title="c12">s1</font>,<font color="Maroon" title="c14">k</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">p</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c12">s1</font></span>)</span>,<font color="Maroon" title="c12">s1</font>,<font color="Maroon" title="c14">k</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> &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="c10">s2</font></span>)</span>,<font color="Maroon" title="c10">s2</font>,<font color="Maroon" title="c14">k</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">p</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c10">s2</font></span>)</span>,<font color="Maroon" title="c10">s2</font>,<font color="Maroon" title="c14">k</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_3.html#T15" target="_self" title="SCMFSA_3:th.15">Th15</a>, <a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></span>;<br/>
<span class="kw">hence </span><a NAME="E31:18_1"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c12">s1</font></span>)</span>,<font color="Maroon" title="c12">s1</font>,<font color="Maroon" title="c14">k</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</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="c10">s2</font></span>)</span>,<font color="Maroon" title="c10">s2</font>,<font color="Maroon" title="c14">k</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">p</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E24:18_1"><span class="lab"><font color="Green" title="E29">A28</font></span></a>, <a class="txt" href="#E29:18_1"><span class="lab"><font color="Green" title="E33">A30</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E19:18"/>
contradiction
 ; <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>
