<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c1">s</font> be   <a href="scmfsa_1.html#NM1" title="SCMFSA_1:NM.1">SCM+FSA-State</a>;<br/><b>let </b><font color="Maroon" title="c2">s'</font> be   <a href="ami_2.html#NM1" title="AMI_2:NM.1">SCM-State</a>;<br/>



<a NAME="E1:34"/><i><font color="Green" title="E17">A1</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <a href="scmfsa_1.html#K7" title="SCMFSA_1:func.7">SCM+FSA-OK</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_1.html#K2" title="SCMFSA_1:func.2">SCM+FSA-Memory</a> 
 
<b>by </b><i><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c3">f</font> =  <a href="scmfsa_1.html#K7" title="SCMFSA_1:func.7">SCM+FSA-OK</a>  as  <a href="relat_1.html#V2" title="RELAT_1:attr.2">non-empty</a>  <a href="pboole.html#M1" title="PBOOLE:mode.1">ManySortedSet</a> of  <a href="scmfsa_1.html#K2" title="SCMFSA_1:func.2">SCM+FSA-Memory</a>  <b>by </b><i><a class="ref" href="pboole.html#D3" title="PBOOLE:def.3">PBOOLE:def 3</a></i>;<br/>
<i><font color="Green" title="E18">A2</font></i>:  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c2">s'</font> = 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <a href="ami_2.html#K8" title="AMI_2:func.8">SCM-OK</a> 
<b>by </b><i><a class="ref" href="card_3.html#T18" title="CARD_3:th.18">CARD_3:18</a></i>
<br/>.= 
 <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Memory</a> 
<b>by </b><i><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>
;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="34_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c4">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>assume </b><a NAME="E1:34_2"/><i><font color="Green" title="E19">A3</font></i>: 
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c2">s'</font>
 ;<br/><a NAME="E2:34_2"/><b>then </b><i><font color="Green" title="E20">A4</font></i>: 
( <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  or <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_2.html#K6" title="AMI_2:func.6">SCM-Instr-Loc</a>  )
 <b>by </b><i><a class="txt" href="scmfsa_1.html#E3:34"><i><font color="Green" title="E18">A2</font></i></a>, <a class="ref" href="ami_3.html#D1" title="AMI_3:def.1">AMI_3:def 1</a>, <a class="ref" href="ami_5.html#T23" title="AMI_5:th.23">AMI_5:23</a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="34_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:34_2_1"/>
( <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> or <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  or <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_2.html#K6" title="AMI_2:func.6">SCM-Instr-Loc</a>  )
 </span><b>by </b><i><a class="txt" href="scmfsa_1.html#E2:34_2"><i><font color="Green" title="E20">A4</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="34_2_1_1"><b>suppose </b></a><a NAME="E1:34_2_1_1"/><i><font color="Green" title="E21">A5</font></i>: 
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 ;<br/><div class="add"><a NAME="E2:34_2_1_1"/><b>then </b><i><font color="Green" title="E22">A6</font></i>: 
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> 
 <b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c5">a</font> = <font color="Maroon" title="c4">x</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Memory</a>  <b>by </b><i><a class="txt" href="scmfsa_1.html#E3:34"><i><font color="Green" title="E18">A2</font></i></a>, <a class="txt" href="scmfsa_1.html#E1:34_2"><i><font color="Green" title="E19">A3</font></i></a></i>;<br/><a NAME="E4:34_2_1_1"/>
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <a href="ami_2.html#K8" title="AMI_2:func.8">SCM-OK</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Memory</a> 
 <b>by </b><i><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>;<br/><b>then </b><i><font color="Green" title="E23">A7</font></i>:  <a href="card_3.html#K5" title="CARD_3:func.5">pi</a> <span class="p1">(<span class="default"><a href="card_3.html#K4" title="CARD_3:func.4">product</a> <a href="ami_2.html#K8" title="AMI_2:func.8">SCM-OK</a> </span>)</span>,<font color="Maroon" title="c5">a</font> = 
<a href="ami_2.html#K8" title="AMI_2:func.8">SCM-OK</a>  <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">a</font>
<b>by </b><i><a class="ref" href="card_3.html#T22" title="CARD_3:th.22">CARD_3:22</a></i>
<br/>.= 
 <a href="ami_2.html#K6" title="AMI_2:func.6">SCM-Instr-Loc</a> 
<b>by </b><i><a class="txt" href="scmfsa_1.html#E2:34_2_1_1"><i><font color="Green" title="E22">A6</font></i></a>, <a class="ref" href="ami_2.html#T7" title="AMI_2:th.7">AMI_2:7</a>, <a class="ref" href="ami_3.html#T4" title="AMI_3:th.4">AMI_3:4</a></i>
;<br/><a NAME="E6:34_2_1_1"/>
<font color="Maroon" title="c2">s'</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="card_3.html#K5" title="CARD_3:func.5">pi</a> <span class="p1">(<span class="default"><a href="card_3.html#K4" title="CARD_3:func.4">product</a> <a href="ami_2.html#K8" title="AMI_2:func.8">SCM-OK</a> </span>)</span>,<font color="Maroon" title="c5">a</font>
 <b>by </b><i><a class="ref" href="card_3.html#D6" title="CARD_3:def.6">CARD_3:def 6</a></i>;<br/><b>hence </b><a NAME="E7:34_2_1_1"/>
<font color="Maroon" title="c2">s'</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x</font>
 <b>by </b><i><a class="txt" href="scmfsa_1.html#E1:34_2_1_1"><i><font color="Green" title="E21">A5</font></i></a>, <a class="txt" href="scmfsa_1.html#E5:34_2_1_1"><i><font color="Green" title="E23">A7</font></i></a>, <a class="ref" href="scmfsa_1.html#T9" target="_self" title="SCMFSA_1:th.9">Th9</a>, <a class="ref" href="ami_3.html#T4" title="AMI_3:th.4">AMI_3:4</a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="34_2_1_2"><b>suppose </b></a><a NAME="E1:34_2_1_2"/><i><font color="Green" title="E21">A8</font></i>: 
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> 
 ;<br/><div class="add"><a NAME="E2:34_2_1_2"/><b>then </b><i><font color="Green" title="E22">A9</font></i>: 
<a href="scmfsa_1.html#K7" title="SCMFSA_1:func.7">SCM+FSA-OK</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> 
 <b>by </b><i><a class="ref" href="scmfsa_1.html#T10" target="_self" title="SCMFSA_1:th.10">Th10</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c5">a</font> = <font color="Maroon" title="c4">x</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Memory</a>  <b>by </b><i><a class="txt" href="scmfsa_1.html#E3:34"><i><font color="Green" title="E18">A2</font></i></a>, <a class="txt" href="scmfsa_1.html#E1:34_2"><i><font color="Green" title="E19">A3</font></i></a></i>;<br/><a NAME="E4:34_2_1_2"/>
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <a href="ami_2.html#K8" title="AMI_2:func.8">SCM-OK</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Memory</a> 
 <b>by </b><i><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>;<br/><a NAME="E5:34_2_1_2"/><b>then </b><i><font color="Green" title="E23">A10</font></i>: 
 <a href="card_3.html#K5" title="CARD_3:func.5">pi</a> <span class="p1">(<span class="default"><a href="card_3.html#K4" title="CARD_3:func.4">product</a> <a href="ami_2.html#K8" title="AMI_2:func.8">SCM-OK</a> </span>)</span>,<font color="Maroon" title="c5">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="ami_2.html#K8" title="AMI_2:func.8">SCM-OK</a>  <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">a</font>
 <b>by </b><i><a class="ref" href="card_3.html#T22" title="CARD_3:th.22">CARD_3:22</a></i>;<br/><a NAME="E6:34_2_1_2"/>
<font color="Maroon" title="c2">s'</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="card_3.html#K5" title="CARD_3:func.5">pi</a> <span class="p1">(<span class="default"><a href="card_3.html#K4" title="CARD_3:func.4">product</a> <a href="ami_2.html#K8" title="AMI_2:func.8">SCM-OK</a> </span>)</span>,<font color="Maroon" title="c5">a</font>
 <b>by </b><i><a class="ref" href="card_3.html#D6" title="CARD_3:def.6">CARD_3:def 6</a></i>;<br/><b>hence </b><a NAME="E7:34_2_1_2"/>
<font color="Maroon" title="c2">s'</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x</font>
 <b>by </b><i><a class="txt" href="scmfsa_1.html#E1:34_2_1_2"><i><font color="Green" title="E21">A8</font></i></a>, <a class="txt" href="scmfsa_1.html#E2:34_2_1_2"><i><font color="Green" title="E22">A9</font></i></a>, <a class="txt" href="scmfsa_1.html#E5:34_2_1_2"><i><font color="Green" title="E23">A10</font></i></a>, <a class="ref" href="ami_2.html#T10" title="AMI_2:th.10">AMI_2:10</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="34_2_1_3"><b>suppose </b></a><a NAME="E1:34_2_1_3"/><i><font color="Green" title="E21">A11</font></i>: 
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_2.html#K6" title="AMI_2:func.6">SCM-Instr-Loc</a> 
 ;<br/><div class="add"><a NAME="E2:34_2_1_3"/><b>then </b><i><font color="Green" title="E22">A12</font></i>: 
<a href="ami_2.html#K8" title="AMI_2:func.8">SCM-OK</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_2.html#K7" title="AMI_2:func.7">SCM-Instr</a> 
 <b>by </b><i><a class="ref" href="ami_2.html#T11" title="AMI_2:th.11">AMI_2:11</a></i>;<br/><a NAME="E3:34_2_1_3"/><i><font color="Green" title="E23">A13</font></i>: 
<a href="scmfsa_1.html#K7" title="SCMFSA_1:func.7">SCM+FSA-OK</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_1.html#K6" title="SCMFSA_1:func.6">SCM+FSA-Instr</a> 
 <b>by </b><i><a class="txt" href="scmfsa_1.html#E1:34_2_1_3"><i><font color="Green" title="E21">A11</font></i></a>, <a class="ref" href="scmfsa_1.html#T11" target="_self" title="SCMFSA_1:th.11">Th11</a></i>;<br/><a NAME="E4:34_2_1_3"/>
 <a href="scmfsa_1.html#K6" title="SCMFSA_1:func.6">SCM+FSA-Instr</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="ami_2.html#K7" title="AMI_2:func.7">SCM-Instr</a>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><span class="p2">{<span class="default"> <span class="p3"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">J</font>,<span class="p4"><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">&lt;*</a><span class="default"><font color="Olive" title="b2">c</font>,<font color="Olive" title="b4">f2</font>,<font color="Olive" title="b3">b</font></span><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> where <font color="Olive" title="b1">J</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="card_1.html#K6" title="CARD_1:func.6">Segm</a> 13, <font color="Olive" title="b2">c</font>, <font color="Olive" title="b3">b</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="scmfsa_1.html#K3" title="SCMFSA_1:func.3">SCM+FSA-Data-Loc</a> , <font color="Olive" title="b4">f2</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="scmfsa_1.html#K4" title="SCMFSA_1:func.4">SCM+FSA-Data*-Loc</a>  : <font color="Olive" title="b1">J</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">9,10</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> </span>}</span>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2">{<span class="default"> <span class="p3"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">K</font>,<span class="p4"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Olive" title="b2">c1</font>,<font color="Olive" title="b3">f1</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> where <font color="Olive" title="b1">K</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="card_1.html#K6" title="CARD_1:func.6">Segm</a> 13, <font color="Olive" title="b2">c1</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="scmfsa_1.html#K3" title="SCMFSA_1:func.3">SCM+FSA-Data-Loc</a> , <font color="Olive" title="b3">f1</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="scmfsa_1.html#K4" title="SCMFSA_1:func.4">SCM+FSA-Data*-Loc</a>  : <font color="Olive" title="b1">K</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">11,12</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> </span>}</span> </span>)</span>
 <b>by </b><i><a class="ref" href="xboole_1.html#T4" title="XBOOLE_1:th.4">XBOOLE_1:4</a></i>;<br/><a NAME="E5:34_2_1_3"/><b>then </b><i><font color="Green" title="E24">A14</font></i>: 
 <a href="ami_2.html#K7" title="AMI_2:func.7">SCM-Instr</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="scmfsa_1.html#K6" title="SCMFSA_1:func.6">SCM+FSA-Instr</a> 
 <b>by </b><i><a class="ref" href="xboole_1.html#T7" title="XBOOLE_1:th.7">XBOOLE_1:7</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c5">a</font> = <font color="Maroon" title="c4">x</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Memory</a>  <b>by </b><i><a class="txt" href="scmfsa_1.html#E3:34"><i><font color="Green" title="E18">A2</font></i></a>, <a class="txt" href="scmfsa_1.html#E1:34_2"><i><font color="Green" title="E19">A3</font></i></a></i>;<br/><a NAME="E7:34_2_1_3"/>
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <a href="ami_2.html#K8" title="AMI_2:func.8">SCM-OK</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Memory</a> 
 <b>by </b><i><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>;<br/><a NAME="E8:34_2_1_3"/><b>then </b><i><font color="Green" title="E25">A15</font></i>: 
 <a href="card_3.html#K5" title="CARD_3:func.5">pi</a> <span class="p1">(<span class="default"><a href="card_3.html#K4" title="CARD_3:func.4">product</a> <a href="ami_2.html#K8" title="AMI_2:func.8">SCM-OK</a> </span>)</span>,<font color="Maroon" title="c5">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="ami_2.html#K8" title="AMI_2:func.8">SCM-OK</a>  <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">a</font>
 <b>by </b><i><a class="ref" href="card_3.html#T22" title="CARD_3:th.22">CARD_3:22</a></i>;<br/><a NAME="E9:34_2_1_3"/>
<font color="Maroon" title="c2">s'</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="card_3.html#K5" title="CARD_3:func.5">pi</a> <span class="p1">(<span class="default"><a href="card_3.html#K4" title="CARD_3:func.4">product</a> <a href="ami_2.html#K8" title="AMI_2:func.8">SCM-OK</a> </span>)</span>,<font color="Maroon" title="c5">a</font>
 <b>by </b><i><a class="ref" href="card_3.html#D6" title="CARD_3:def.6">CARD_3:def 6</a></i>;<br/><b>hence </b><a NAME="E10:34_2_1_3"/>
<font color="Maroon" title="c2">s'</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x</font>
 <b>by </b><i><a class="txt" href="scmfsa_1.html#E2:34_2_1_3"><i><font color="Green" title="E22">A12</font></i></a>, <a class="txt" href="scmfsa_1.html#E3:34_2_1_3"><i><font color="Green" title="E23">A13</font></i></a>, <a class="txt" href="scmfsa_1.html#E5:34_2_1_3"><i><font color="Green" title="E24">A14</font></i></a>, <a class="txt" href="scmfsa_1.html#E8:34_2_1_3"><i><font color="Green" title="E25">A15</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<a NAME="E5:34"/><b>then </b><i><font color="Green" title="E19">A16</font></i>: 
<font color="Maroon" title="c1">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c2">s'</font> is   <a href="scmfsa_1.html#NM1" title="SCMFSA_1:NM.1">SCM+FSA-State</a>
 
<b>by </b><i><a class="txt" href="scmfsa_1.html#E1:34"><i><font color="Green" title="E17">A1</font></i></a>, <a class="txt" href="scmfsa_1.html#E3:34"><i><font color="Green" title="E18">A2</font></i></a>, <a class="ref" href="scmfsa_1.html#T1" target="_self" title="SCMFSA_1:th.1">Th1</a>, <a class="ref" href="pre_circ.html#T9" title="PRE_CIRC:th.9">PRE_CIRC:9</a></i>;<br/>
<a NAME="E6:34"/><i><font color="Green" title="E20">A17</font></i>: 
<font color="Maroon" title="c1">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="card_3.html#K4" title="CARD_3:func.4">product</a> <a href="scmfsa_1.html#K7" title="SCMFSA_1:func.7">SCM+FSA-OK</a> 
 
;<br/>
<a NAME="E7:34"/>
 <a href="card_3.html#K4" title="CARD_3:func.4">product</a> <a href="scmfsa_1.html#K7" title="SCMFSA_1:func.7">SCM+FSA-OK</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="card_3.html#K8" title="CARD_3:func.8">sproduct</a> <a href="scmfsa_1.html#K7" title="SCMFSA_1:func.7">SCM+FSA-OK</a> 
 
<b>by </b><i><a class="ref" href="card_3.html#T67" title="CARD_3:th.67">CARD_3:67</a></i>;<br/>
<a NAME="E8:34"/><b>then </b>
<font color="Maroon" title="c1">s</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">SCM+FSA-Instr-Loc</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="card_3.html#K8" title="CARD_3:func.8">sproduct</a> <a href="scmfsa_1.html#K7" title="SCMFSA_1:func.7">SCM+FSA-OK</a> 
 
<b>by </b><i><a class="txt" href="scmfsa_1.html#E6:34"><i><font color="Green" title="E20">A17</font></i></a>, <a class="ref" href="card_3.html#T81" title="CARD_3:th.81">CARD_3:81</a></i>;<br/>
<b>hence </b><a NAME="E9:34"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c2">s'</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">s</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">SCM+FSA-Instr-Loc</a> </span>)</span> is   <a href="scmfsa_1.html#NM1" title="SCMFSA_1:NM.1">SCM+FSA-State</a>
 <b>by </b><i><a class="txt" href="scmfsa_1.html#E5:34"><i><font color="Green" title="E19">A16</font></i></a>, <a class="ref" href="card_3.html#T69" title="CARD_3:th.69">CARD_3:69</a></i>;<br/>


</div>
