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

<b>let </b><font color="Maroon">I</font> be   <a href="scmfsa6a.html#NM1">Macro-Instruction</a>, <font color="Maroon">J</font> be   <a href="scmfsa6a.html#NM1">Macro-Instruction</a>;<br/><b>let </b><font color="Maroon">s</font> be   <a href="ami_1.html#NM4">State</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> ;<br/>



<b>set </b><font color="Maroon">s1</font> = <font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <font color="Maroon">I</font>;<br/>
<b>assume </b><a NAME="E1:53"/><i><font color="Green">E29</font></i>: 
 <a href="scmfsa6a.html#K3" target="_self">Initialized</a> <font color="Maroon">J</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">s</font>
 ;<br/>

<a NAME="E2:53"/><b>then </b><i><font color="Green">E30</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" target="_self">Initialized</a> <font color="Maroon">J</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">s</font>
 
<b>by </b><i><a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>;<br/>
<span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">J</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" target="_self">Initialized</a> <font color="Maroon">I</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">J</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span><a href="domain_1.html#K6">}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">I</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">J</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span><a href="domain_1.html#K6">}</a></span> <a href="subset_1.html#K4">\/</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">I</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T4">XBOOLE_1:4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">J</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2">(<span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span><a href="domain_1.html#K6">}</a></span> <a href="subset_1.html#K4">\/</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">I</font></span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T4">XBOOLE_1:4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">J</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">I</font></span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T4">XBOOLE_1:4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" target="_self">Initialized</a> <font color="Maroon">J</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">I</font></span>)</span>
<b>by </b><i/>
;<br/>
<a NAME="E4:53"/><b>then </b>
<span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">J</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" target="_self">Initialized</a> <font color="Maroon">I</font></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">s</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">I</font></span>)</span>
 
<b>by </b><i><a class="txt" href="scmfsa6a.html#E6:53"><i><font color="Green">E31</font></i></a>, <a class="ref" href="xboole_1.html#T13">XBOOLE_1:13</a></i>;<br/>
<a NAME="E5:53"/><b>then </b>
<span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">J</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" target="_self">Initialized</a> <font color="Maroon">I</font></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <font color="Maroon">I</font></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_4.html#D1">FUNCT_4:def 1</a></i>;<br/>
<a NAME="E6:53"/><b>then </b><i><font color="Green">E31</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" target="_self">Initialized</a> <font color="Maroon">I</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <font color="Maroon">I</font></span>)</span>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T11">XBOOLE_1:11</a></i>;<br/>
<div><i><font color="Green">E32</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="53_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:53_2"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" target="_self">Initialized</a> <font color="Maroon">I</font></span>)</span>
 ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="53_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:53_2_1"/>
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">I</font> or <font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K4">intloc</a> 0 or <font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a>  )
 </span><b>by </b><i>, </i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="53_2_1_1"><b>suppose </b></a><a NAME="E1:53_2_1_1"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">I</font>
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" target="_self">Initialized</a> <font color="Maroon">I</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
<font color="Maroon">I</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <font color="Maroon">I</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i><a class="ref" href="scmfsa6a.html#T8" target="_self">Th8</a>, <a class="ref" href="funct_4.html#T14">FUNCT_4:14</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="53_2_1_2"><b>suppose </b></a><a NAME="E1:53_2_1_2"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K4">intloc</a> 0
 ;<br/><div class="add"><a NAME="E2:53_2_1_2"/><b>then </b><i><font color="Green">E40</font></i>: 
not <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">I</font>
 <b>by </b><i/>;<br/><a NAME="E3:53_2_1_2"/><i><font color="Green">E41</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" target="_self">Initialized</a> <font color="Maroon">J</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa6a.html#T8" target="_self">Th8</a>, </i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" target="_self">Initialized</a> <font color="Maroon">I</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
1
<b>by </b><i><a class="ref" href="scmfsa6a.html#T8" target="_self">Th8</a>, </i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" target="_self">Initialized</a> <font color="Maroon">J</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i><a class="ref" href="scmfsa6a.html#T8" target="_self">Th8</a>, </i>
<br/>.= 
<font color="Maroon">s</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i><a class="txt" href="scmfsa6a.html#E2:53"><i><font color="Green">E30</font></i></a>, , <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <font color="Maroon">I</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i><a class="ref" href="scmfsa6a.html#T9" target="_self">Th9</a>, <a class="ref" href="funct_4.html#T12">FUNCT_4:12</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="53_2_1_3"><b>suppose </b></a><a NAME="E1:53_2_1_3"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> 
 ;<br/><div class="add"><a NAME="E2:53_2_1_3"/><b>then </b><i><font color="Green">E43</font></i>: 
not <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">I</font>
 <b>by </b><i/>;<br/><a NAME="E3:53_2_1_3"/><i><font color="Green">E44</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" target="_self">Initialized</a> <font color="Maroon">J</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa6a.html#T8" target="_self">Th8</a>, </i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" target="_self">Initialized</a> <font color="Maroon">I</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
 <a href="scmfsa_2.html#K5">insloc</a> 0
<b>by </b><i><a class="ref" href="scmfsa6a.html#T8" target="_self">Th8</a>, </i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" target="_self">Initialized</a> <font color="Maroon">J</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i><a class="ref" href="scmfsa6a.html#T8" target="_self">Th8</a>, </i>
<br/>.= 
<font color="Maroon">s</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i><a class="txt" href="scmfsa6a.html#E2:53"><i><font color="Green">E30</font></i></a>, , <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <font color="Maroon">I</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i><a class="ref" href="scmfsa6a.html#T9" target="_self">Th9</a>, <a class="ref" href="funct_4.html#T12">FUNCT_4:12</a></i>
;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<a NAME="E8:53"/><i><font color="Green">E45</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <font color="Maroon">I</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">s</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">I</font></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_4.html#D1">FUNCT_4:def 1</a></i>;<br/>
<a NAME="E9:53"/><i><font color="Green">E91</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" target="_self">Initialized</a> <font color="Maroon">I</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">s</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" target="_self">Initialized</a> <font color="Maroon">I</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_4.html#D1">FUNCT_4:def 1</a></i>;<br/>
<a NAME="E10:53"/>
<font color="Maroon">I</font> <a href="tarski.html#R1">c=</a>  <a href="scmfsa6a.html#K3" target="_self">Initialized</a> <font color="Maroon">I</font>
 
<b>by </b><i/>;<br/>
<a NAME="E11:53"/><b>then </b><i><font color="Green">E92</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">I</font> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" target="_self">Initialized</a> <font color="Maroon">I</font></span>)</span>
 
<b>by </b><i><a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>;<br/>
<a NAME="E12:53"/><b>then </b><i><font color="Green">E93</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <font color="Maroon">I</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" target="_self">Initialized</a> <font color="Maroon">I</font></span>)</span></span>)</span>
 
<b>by </b><i>, <a class="ref" href="scmfsa6a.html#T8" target="_self">Th8</a>, <a class="ref" href="xboole_1.html#T9">XBOOLE_1:9</a></i>;<br/>
<a NAME="E13:53"/>
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" target="_self">Initialized</a> <font color="Maroon">I</font></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">s</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">s</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">I</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scmfsa6a.html#E7:53"><i><font color="Green">E32</font></i></a>, , <a class="ref" href="scmfsa6a.html#T8" target="_self">Th8</a>, <a class="ref" href="xboole_1.html#T9">XBOOLE_1:9</a></i>;<br/>
<a NAME="E14:53"/><b>then </b>
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" target="_self">Initialized</a> <font color="Maroon">I</font></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">s</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">s</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">I</font></span>)</span>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T4">XBOOLE_1:4</a></i>;<br/>
<a NAME="E15:53"/><b>then </b><i><font color="Green">E94</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" target="_self">Initialized</a> <font color="Maroon">I</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <font color="Maroon">I</font></span>)</span>
 
<b>by </b><i>, , <a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="53_3"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:53_3"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" target="_self">Initialized</a> <font color="Maroon">I</font></span>)</span></span>)</span>
 ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="53_3_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:53_3_1"/>
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" target="_self">Initialized</a> <font color="Maroon">I</font></span>)</span> or  not <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" target="_self">Initialized</a> <font color="Maroon">I</font></span>)</span> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="53_3_1_1"><b>suppose </b></a><a NAME="E1:53_3_1_1"/><i><font color="Green">E95</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" target="_self">Initialized</a> <font color="Maroon">I</font></span>)</span>
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" target="_self">Initialized</a> <font color="Maroon">I</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
<span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" target="_self">Initialized</a> <font color="Maroon">I</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i><a class="ref" href="funct_4.html#T14">FUNCT_4:14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <font color="Maroon">I</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i>, <a class="ref" href="scmfsa6a.html#T10" target="_self">Th10</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="53_3_1_2"><b>suppose </b></a><a NAME="E1:53_3_1_2"/><i><font color="Green">E96</font></i>: 
not <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" target="_self">Initialized</a> <font color="Maroon">I</font></span>)</span>
 ;<br/><div class="add"><a NAME="E2:53_3_1_2"/><b>then </b><i><font color="Green">E97</font></i>: 
not <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">I</font>
 <b>by </b><i><a class="ref" href="scmfsa6a.html#T9" target="_self">Th9</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" target="_self">Initialized</a> <font color="Maroon">I</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
<font color="Maroon">s</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i><a class="ref" href="scmfsa6a.html#T10" target="_self">Th10</a>, <a class="ref" href="funct_4.html#T12">FUNCT_4:12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <font color="Maroon">I</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i>, <a class="ref" href="funct_4.html#T12">FUNCT_4:12</a></i>
;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E17:53"/>
<font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" target="_self">Initialized</a> <font color="Maroon">I</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <font color="Maroon">I</font>
 <b>by </b><i>, <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/>


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