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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="ami_1.html#NM8">InsType</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="amistd_2.html#D11">AMISTD_2:def 11</a><br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:122_1_1_1"/>
( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 0 or <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 1 or <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 2 or <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 3 or <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 4 or <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 5 or <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 6 or <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 7 or <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 8 or <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 9 or <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 10 or <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 11 or <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 12 )
 </span><b>by </b><i><a class="txt" href="scmfsa10.html#E20"><i><font color="Green">Lemma19</font></i></a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_1_1_1_1"><b>suppose </b></a><a NAME="E1:122_1_1_1_1"/><i><font color="Green">E94</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 0
 ;<br/><div class="add"><b>reconsider </b><font color="Maroon">c<sub>2</sub></font> =  <a href="xboole_0.html#K1">{}</a>  as   <a href="funct_1.html#NM1">Function</a> ;<br/><b>take </b>
<font color="Maroon">c<sub>2</sub></font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="amistd_2.html#D2">AMISTD_2:def 2</a><br/><b>thus </b><a NAME="E3:122_1_1_1_1"/>
 <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="card_3.html#K4">product</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E1:122_1_1_1_1"><i><font color="Green">E94</font></i></a>, <a class="ref" href="scmfsa10.html#T30" target="_self">Th30</a>, <a class="ref" href="card_3.html#T19">CARD_3:19</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_1_1_1_2"><b>suppose </b></a><a NAME="E1:122_1_1_1_2"/><i><font color="Green">E94</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 1
 ;<br/><div class="add"><b>take </b>
 <a href="amistd_2.html#K1">PA</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
; <i><font color="Red">:: according to </font></i><a class="ref" href="amistd_2.html#D2">AMISTD_2:def 2</a><br/><b>thus </b><a NAME="E2:122_1_1_1_2"/>
 <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a>  <a href="card_3.html#K4">product</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="amistd_2.html#T9">AMISTD_2:9</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/><b>assume </b><a NAME="E3:122_1_1_1_2"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="card_3.html#K4">product</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 ;<br/><b>then consider </b><font color="Maroon">c<sub>3</sub></font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E5:122_1_1_1_2"/><i><font color="Green">E95</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>and </b><br/><a NAME="E6:122_1_1_1_2"/><i><font color="Green">E96</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E7:122_1_1_1_2"/><i><font color="Green">E97</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> holds <br/><font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="card_3.html#D5">CARD_3:def 5</a></i>;<br/><a NAME="E8:122_1_1_1_2"/><i><font color="Green">E98</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E1:122_1_1_1_2"><i><font color="Green">E94</font></i></a>, <a class="ref" href="scmfsa10.html#T31" target="_self">Th31</a></i>;<br/><a NAME="E9:122_1_1_1_2"/><b>then </b><i><font color="Green">E99</font></i>: 
1 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><a NAME="E10:122_1_1_1_2"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 1
 <b>by </b><i><a class="txt" href="scmfsa10.html#E7:122_1_1_1_2"><i><font color="Green">E97</font></i></a></i>;<br/><a NAME="E11:122_1_1_1_2"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R2">in</a>  <a href="card_3.html#K5">pi</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,1
 <b>by </b><i><a class="txt" href="scmfsa10.html#E9:122_1_1_1_2"><i><font color="Green">E99</font></i></a>, <a class="ref" href="amistd_2.html#D1">AMISTD_2:def 1</a></i>;<br/><b>then consider </b><font color="Maroon">c<sub>4</sub></font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E13:122_1_1_1_2"/><i><font color="Green">E100</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font>
 <b>and </b><br/><a NAME="E14:122_1_1_1_2"/><i><font color="Green">E101</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 1
 <b>by </b><i><a class="ref" href="card_3.html#D6">CARD_3:def 6</a></i>;<br/><a NAME="E15:122_1_1_1_2"/><i><font color="Green">E102</font></i>: 
2 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E8:122_1_1_1_2"><i><font color="Green">E98</font></i></a>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><a NAME="E16:122_1_1_1_2"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 2
 <b>by </b><i><a class="txt" href="scmfsa10.html#E7:122_1_1_1_2"><i><font color="Green">E97</font></i></a></i>;<br/><a NAME="E17:122_1_1_1_2"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R2">in</a>  <a href="card_3.html#K5">pi</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,2
 <b>by </b><i><a class="txt" href="scmfsa10.html#E15:122_1_1_1_2"><i><font color="Green">E102</font></i></a>, <a class="ref" href="amistd_2.html#D1">AMISTD_2:def 1</a></i>;<br/><b>then consider </b><font color="Maroon">c<sub>5</sub></font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E19:122_1_1_1_2"/><i><font color="Green">E103</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font>
 <b>and </b><br/><a NAME="E20:122_1_1_1_2"/><i><font color="Green">E104</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 2
 <b>by </b><i><a class="ref" href="card_3.html#D6">CARD_3:def 6</a></i>;<br/><b>consider </b><font color="Maroon">c<sub>6</sub></font> being   <a href="ami_1.html#NM3">Instruction</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> <b> such that </b><br/><a NAME="E22:122_1_1_1_2"/><i><font color="Green">E105</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">c<sub>6</sub></font>
 <b>and </b><br/><a NAME="E23:122_1_1_1_2"/><i><font color="Green">E106</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E13:122_1_1_1_2"><i><font color="Green">E100</font></i></a></i>;<br/><b>consider </b><font color="Maroon">c<sub>7</sub></font>, <font color="Maroon">c<sub>8</sub></font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E25:122_1_1_1_2"/><i><font color="Green">E107</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> <a href="scmfsa_2.html#K8">:=</a> <font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E1:122_1_1_1_2"><i><font color="Green">E94</font></i></a>, <a class="txt" href="scmfsa10.html#E23:122_1_1_1_2"><i><font color="Green">E106</font></i></a>, <a class="ref" href="scmfsa_2.html#T54">SCMFSA_2:54</a></i>;<br/><a NAME="E26:122_1_1_1_2"/><i><font color="Green">E108</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E22:122_1_1_1_2"><i><font color="Green">E105</font></i></a>, <a class="txt" href="scmfsa10.html#E25:122_1_1_1_2"><i><font color="Green">E107</font></i></a>, <a class="ref" href="scmfsa10.html#T18" target="_self">Th18</a></i>;<br/><b>consider </b><font color="Maroon">c<sub>9</sub></font> being   <a href="ami_1.html#NM3">Instruction</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> <b> such that </b><br/><a NAME="E28:122_1_1_1_2"/><i><font color="Green">E109</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">c<sub>9</sub></font>
 <b>and </b><br/><a NAME="E29:122_1_1_1_2"/><i><font color="Green">E110</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E19:122_1_1_1_2"><i><font color="Green">E103</font></i></a></i>;<br/><b>consider </b><font color="Maroon">c<sub>10</sub></font>, <font color="Maroon">c<sub>11</sub></font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E31:122_1_1_1_2"/><i><font color="Green">E111</font></i>: 
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>10</sub></font> <a href="scmfsa_2.html#K8">:=</a> <font color="Maroon">c<sub>11</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E1:122_1_1_1_2"><i><font color="Green">E94</font></i></a>, <a class="txt" href="scmfsa10.html#E29:122_1_1_1_2"><i><font color="Green">E110</font></i></a>, <a class="ref" href="scmfsa_2.html#T54">SCMFSA_2:54</a></i>;<br/><a NAME="E32:122_1_1_1_2"/><i><font color="Green">E112</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E28:122_1_1_1_2"><i><font color="Green">E109</font></i></a>, <a class="txt" href="scmfsa10.html#E31:122_1_1_1_2"><i><font color="Green">E111</font></i></a>, <a class="ref" href="scmfsa10.html#T18" target="_self">Th18</a></i>;<br/><a NAME="E33:122_1_1_1_2"/><i><font color="Green">E113</font></i>: 
 <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i><a class="ref" href="finseq_1.html#T4">FINSEQ_1:4</a>, <a class="ref" href="finseq_3.html#T29">FINSEQ_3:29</a></i>;<br/><a NAME="E34:122_1_1_1_2"/>
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span> holds <br/><span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="122_1_1_1_2_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>12</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:122_1_1_1_2_1"/><i><font color="Green">E114</font></i>: 
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span>
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_1_1_1_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:122_1_1_1_2_1_1"/>
( <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> 1 or <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> 2 )
 </span><b>by </b><i><a class="txt" href="scmfsa10.html#E1:122_1_1_1_2_1"><i><font color="Green">E114</font></i></a>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_1_1_1_2_1_1_1"><b>suppose </b></a><a NAME="E1:122_1_1_1_2_1_1_1"/><i><font color="Green">E115</font></i>: 
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> 1
 ;<br/><div class="add"><span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="funct_1.html#K1">.</a> 1 = 
<font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 1
<b>by </b><i><a class="txt" href="scmfsa10.html#E14:122_1_1_1_2"><i><font color="Green">E101</font></i></a>, <a class="txt" href="scmfsa10.html#E26:122_1_1_1_2"><i><font color="Green">E108</font></i></a>, <a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
;<br/><b>hence </b><a NAME="E3:122_1_1_1_2_1_1_1"/>
<span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E1:122_1_1_1_2_1_1_1"><i><font color="Green">E115</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_1_1_1_2_1_1_2"><b>suppose </b></a><a NAME="E1:122_1_1_1_2_1_1_2"/><i><font color="Green">E115</font></i>: 
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> 2
 ;<br/><div class="add"><span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="funct_1.html#K1">.</a> 2 = 
<font color="Maroon">c<sub>11</sub></font>
<b>by </b><i><a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 2
<b>by </b><i><a class="txt" href="scmfsa10.html#E20:122_1_1_1_2"><i><font color="Green">E104</font></i></a>, <a class="txt" href="scmfsa10.html#E32:122_1_1_1_2"><i><font color="Green">E112</font></i></a>, <a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
;<br/><b>hence </b><a NAME="E3:122_1_1_1_2_1_1_2"/>
<span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E1:122_1_1_1_2_1_1_2"><i><font color="Green">E115</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div><a NAME="E35:122_1_1_1_2"/><b>then </b><i><font color="Green">E114</font></i>: 
<span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E6:122_1_1_1_2"><i><font color="Green">E96</font></i></a>, <a class="txt" href="scmfsa10.html#E8:122_1_1_1_2"><i><font color="Green">E98</font></i></a>, <a class="txt" href="scmfsa10.html#E33:122_1_1_1_2"><i><font color="Green">E113</font></i></a>, <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/><a NAME="E36:122_1_1_1_2"/>
(  <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="scmfsa_2.html#K8">:=</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="hidden.html#R1">=</a> 1 &amp;  <a href="amistd_2.html#K4">AddressPart</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="scmfsa_2.html#K8">:=</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span> )
 <b>by </b><i><a class="ref" href="scmfsa10.html#T18" target="_self">Th18</a>, <a class="ref" href="scmfsa_2.html#T42">SCMFSA_2:42</a></i>;<br/><b>hence </b><a NAME="E37:122_1_1_1_2"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E1:122_1_1_1_2"><i><font color="Green">E94</font></i></a>, <a class="txt" href="scmfsa10.html#E5:122_1_1_1_2"><i><font color="Green">E95</font></i></a>, <a class="txt" href="scmfsa10.html#E35:122_1_1_1_2"><i><font color="Green">E114</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_1_1_1_3"><b>suppose </b></a><a NAME="E1:122_1_1_1_3"/><i><font color="Green">E94</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 2
 ;<br/><div class="add"><b>take </b>
 <a href="amistd_2.html#K1">PA</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
; <i><font color="Red">:: according to </font></i><a class="ref" href="amistd_2.html#D2">AMISTD_2:def 2</a><br/><b>thus </b><a NAME="E2:122_1_1_1_3"/>
 <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a>  <a href="card_3.html#K4">product</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="amistd_2.html#T9">AMISTD_2:9</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/><b>assume </b><a NAME="E3:122_1_1_1_3"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="card_3.html#K4">product</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 ;<br/><b>then consider </b><font color="Maroon">c<sub>3</sub></font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E5:122_1_1_1_3"/><i><font color="Green">E95</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>and </b><br/><a NAME="E6:122_1_1_1_3"/><i><font color="Green">E96</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E7:122_1_1_1_3"/><i><font color="Green">E97</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> holds <br/><font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="card_3.html#D5">CARD_3:def 5</a></i>;<br/><a NAME="E8:122_1_1_1_3"/><i><font color="Green">E98</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E1:122_1_1_1_3"><i><font color="Green">E94</font></i></a>, <a class="ref" href="scmfsa10.html#T32" target="_self">Th32</a></i>;<br/><a NAME="E9:122_1_1_1_3"/><b>then </b><i><font color="Green">E99</font></i>: 
1 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><a NAME="E10:122_1_1_1_3"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 1
 <b>by </b><i><a class="txt" href="scmfsa10.html#E7:122_1_1_1_3"><i><font color="Green">E97</font></i></a></i>;<br/><a NAME="E11:122_1_1_1_3"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R2">in</a>  <a href="card_3.html#K5">pi</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,1
 <b>by </b><i><a class="txt" href="scmfsa10.html#E9:122_1_1_1_3"><i><font color="Green">E99</font></i></a>, <a class="ref" href="amistd_2.html#D1">AMISTD_2:def 1</a></i>;<br/><b>then consider </b><font color="Maroon">c<sub>4</sub></font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E13:122_1_1_1_3"/><i><font color="Green">E100</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font>
 <b>and </b><br/><a NAME="E14:122_1_1_1_3"/><i><font color="Green">E101</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 1
 <b>by </b><i><a class="ref" href="card_3.html#D6">CARD_3:def 6</a></i>;<br/><a NAME="E15:122_1_1_1_3"/><i><font color="Green">E102</font></i>: 
2 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E8:122_1_1_1_3"><i><font color="Green">E98</font></i></a>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><a NAME="E16:122_1_1_1_3"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 2
 <b>by </b><i><a class="txt" href="scmfsa10.html#E7:122_1_1_1_3"><i><font color="Green">E97</font></i></a></i>;<br/><a NAME="E17:122_1_1_1_3"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R2">in</a>  <a href="card_3.html#K5">pi</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,2
 <b>by </b><i><a class="txt" href="scmfsa10.html#E15:122_1_1_1_3"><i><font color="Green">E102</font></i></a>, <a class="ref" href="amistd_2.html#D1">AMISTD_2:def 1</a></i>;<br/><b>then consider </b><font color="Maroon">c<sub>5</sub></font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E19:122_1_1_1_3"/><i><font color="Green">E103</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font>
 <b>and </b><br/><a NAME="E20:122_1_1_1_3"/><i><font color="Green">E104</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 2
 <b>by </b><i><a class="ref" href="card_3.html#D6">CARD_3:def 6</a></i>;<br/><b>consider </b><font color="Maroon">c<sub>6</sub></font> being   <a href="ami_1.html#NM3">Instruction</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> <b> such that </b><br/><a NAME="E22:122_1_1_1_3"/><i><font color="Green">E105</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">c<sub>6</sub></font>
 <b>and </b><br/><a NAME="E23:122_1_1_1_3"/><i><font color="Green">E106</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E13:122_1_1_1_3"><i><font color="Green">E100</font></i></a></i>;<br/><b>consider </b><font color="Maroon">c<sub>7</sub></font>, <font color="Maroon">c<sub>8</sub></font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E25:122_1_1_1_3"/><i><font color="Green">E107</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K9">AddTo</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E1:122_1_1_1_3"><i><font color="Green">E94</font></i></a>, <a class="txt" href="scmfsa10.html#E23:122_1_1_1_3"><i><font color="Green">E106</font></i></a>, <a class="ref" href="scmfsa_2.html#T55">SCMFSA_2:55</a></i>;<br/><a NAME="E26:122_1_1_1_3"/><i><font color="Green">E108</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E22:122_1_1_1_3"><i><font color="Green">E105</font></i></a>, <a class="txt" href="scmfsa10.html#E25:122_1_1_1_3"><i><font color="Green">E107</font></i></a>, <a class="ref" href="scmfsa10.html#T19" target="_self">Th19</a></i>;<br/><b>consider </b><font color="Maroon">c<sub>9</sub></font> being   <a href="ami_1.html#NM3">Instruction</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> <b> such that </b><br/><a NAME="E28:122_1_1_1_3"/><i><font color="Green">E109</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">c<sub>9</sub></font>
 <b>and </b><br/><a NAME="E29:122_1_1_1_3"/><i><font color="Green">E110</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E19:122_1_1_1_3"><i><font color="Green">E103</font></i></a></i>;<br/><b>consider </b><font color="Maroon">c<sub>10</sub></font>, <font color="Maroon">c<sub>11</sub></font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E31:122_1_1_1_3"/><i><font color="Green">E111</font></i>: 
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K9">AddTo</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E1:122_1_1_1_3"><i><font color="Green">E94</font></i></a>, <a class="txt" href="scmfsa10.html#E29:122_1_1_1_3"><i><font color="Green">E110</font></i></a>, <a class="ref" href="scmfsa_2.html#T55">SCMFSA_2:55</a></i>;<br/><a NAME="E32:122_1_1_1_3"/><i><font color="Green">E112</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E28:122_1_1_1_3"><i><font color="Green">E109</font></i></a>, <a class="txt" href="scmfsa10.html#E31:122_1_1_1_3"><i><font color="Green">E111</font></i></a>, <a class="ref" href="scmfsa10.html#T19" target="_self">Th19</a></i>;<br/><a NAME="E33:122_1_1_1_3"/><i><font color="Green">E113</font></i>: 
 <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i><a class="ref" href="finseq_1.html#T4">FINSEQ_1:4</a>, <a class="ref" href="finseq_3.html#T29">FINSEQ_3:29</a></i>;<br/><a NAME="E34:122_1_1_1_3"/>
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span> holds <br/><span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="122_1_1_1_3_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>12</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:122_1_1_1_3_1"/><i><font color="Green">E114</font></i>: 
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span>
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_1_1_1_3_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:122_1_1_1_3_1_1"/>
( <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> 1 or <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> 2 )
 </span><b>by </b><i><a class="txt" href="scmfsa10.html#E1:122_1_1_1_3_1"><i><font color="Green">E114</font></i></a>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_1_1_1_3_1_1_1"><b>suppose </b></a><a NAME="E1:122_1_1_1_3_1_1_1"/><i><font color="Green">E115</font></i>: 
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> 1
 ;<br/><div class="add"><span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="funct_1.html#K1">.</a> 1 = 
<font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 1
<b>by </b><i><a class="txt" href="scmfsa10.html#E14:122_1_1_1_3"><i><font color="Green">E101</font></i></a>, <a class="txt" href="scmfsa10.html#E26:122_1_1_1_3"><i><font color="Green">E108</font></i></a>, <a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
;<br/><b>hence </b><a NAME="E3:122_1_1_1_3_1_1_1"/>
<span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E1:122_1_1_1_3_1_1_1"><i><font color="Green">E115</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_1_1_1_3_1_1_2"><b>suppose </b></a><a NAME="E1:122_1_1_1_3_1_1_2"/><i><font color="Green">E115</font></i>: 
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> 2
 ;<br/><div class="add"><span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="funct_1.html#K1">.</a> 2 = 
<font color="Maroon">c<sub>11</sub></font>
<b>by </b><i><a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 2
<b>by </b><i><a class="txt" href="scmfsa10.html#E20:122_1_1_1_3"><i><font color="Green">E104</font></i></a>, <a class="txt" href="scmfsa10.html#E32:122_1_1_1_3"><i><font color="Green">E112</font></i></a>, <a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
;<br/><b>hence </b><a NAME="E3:122_1_1_1_3_1_1_2"/>
<span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E1:122_1_1_1_3_1_1_2"><i><font color="Green">E115</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div><a NAME="E35:122_1_1_1_3"/><b>then </b><i><font color="Green">E114</font></i>: 
<span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E6:122_1_1_1_3"><i><font color="Green">E96</font></i></a>, <a class="txt" href="scmfsa10.html#E8:122_1_1_1_3"><i><font color="Green">E98</font></i></a>, <a class="txt" href="scmfsa10.html#E33:122_1_1_1_3"><i><font color="Green">E113</font></i></a>, <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/><a NAME="E36:122_1_1_1_3"/>
(  <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K9">AddTo</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="hidden.html#R1">=</a> 2 &amp;  <a href="amistd_2.html#K4">AddressPart</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K9">AddTo</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span> )
 <b>by </b><i><a class="ref" href="scmfsa10.html#T19" target="_self">Th19</a>, <a class="ref" href="scmfsa_2.html#T43">SCMFSA_2:43</a></i>;<br/><b>hence </b><a NAME="E37:122_1_1_1_3"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E1:122_1_1_1_3"><i><font color="Green">E94</font></i></a>, <a class="txt" href="scmfsa10.html#E5:122_1_1_1_3"><i><font color="Green">E95</font></i></a>, <a class="txt" href="scmfsa10.html#E35:122_1_1_1_3"><i><font color="Green">E114</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_1_1_1_4"><b>suppose </b></a><a NAME="E1:122_1_1_1_4"/><i><font color="Green">E94</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 3
 ;<br/><div class="add"><b>take </b>
 <a href="amistd_2.html#K1">PA</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
; <i><font color="Red">:: according to </font></i><a class="ref" href="amistd_2.html#D2">AMISTD_2:def 2</a><br/><b>thus </b><a NAME="E2:122_1_1_1_4"/>
 <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a>  <a href="card_3.html#K4">product</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="amistd_2.html#T9">AMISTD_2:9</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/><b>assume </b><a NAME="E3:122_1_1_1_4"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="card_3.html#K4">product</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 ;<br/><b>then consider </b><font color="Maroon">c<sub>3</sub></font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E5:122_1_1_1_4"/><i><font color="Green">E95</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>and </b><br/><a NAME="E6:122_1_1_1_4"/><i><font color="Green">E96</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E7:122_1_1_1_4"/><i><font color="Green">E97</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> holds <br/><font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="card_3.html#D5">CARD_3:def 5</a></i>;<br/><a NAME="E8:122_1_1_1_4"/><i><font color="Green">E98</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E1:122_1_1_1_4"><i><font color="Green">E94</font></i></a>, <a class="ref" href="scmfsa10.html#T33" target="_self">Th33</a></i>;<br/><a NAME="E9:122_1_1_1_4"/><b>then </b><i><font color="Green">E99</font></i>: 
1 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><a NAME="E10:122_1_1_1_4"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 1
 <b>by </b><i><a class="txt" href="scmfsa10.html#E7:122_1_1_1_4"><i><font color="Green">E97</font></i></a></i>;<br/><a NAME="E11:122_1_1_1_4"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R2">in</a>  <a href="card_3.html#K5">pi</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,1
 <b>by </b><i><a class="txt" href="scmfsa10.html#E9:122_1_1_1_4"><i><font color="Green">E99</font></i></a>, <a class="ref" href="amistd_2.html#D1">AMISTD_2:def 1</a></i>;<br/><b>then consider </b><font color="Maroon">c<sub>4</sub></font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E13:122_1_1_1_4"/><i><font color="Green">E100</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font>
 <b>and </b><br/><a NAME="E14:122_1_1_1_4"/><i><font color="Green">E101</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 1
 <b>by </b><i><a class="ref" href="card_3.html#D6">CARD_3:def 6</a></i>;<br/><a NAME="E15:122_1_1_1_4"/><i><font color="Green">E102</font></i>: 
2 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E8:122_1_1_1_4"><i><font color="Green">E98</font></i></a>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><a NAME="E16:122_1_1_1_4"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 2
 <b>by </b><i><a class="txt" href="scmfsa10.html#E7:122_1_1_1_4"><i><font color="Green">E97</font></i></a></i>;<br/><a NAME="E17:122_1_1_1_4"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R2">in</a>  <a href="card_3.html#K5">pi</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,2
 <b>by </b><i><a class="txt" href="scmfsa10.html#E15:122_1_1_1_4"><i><font color="Green">E102</font></i></a>, <a class="ref" href="amistd_2.html#D1">AMISTD_2:def 1</a></i>;<br/><b>then consider </b><font color="Maroon">c<sub>5</sub></font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E19:122_1_1_1_4"/><i><font color="Green">E103</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font>
 <b>and </b><br/><a NAME="E20:122_1_1_1_4"/><i><font color="Green">E104</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 2
 <b>by </b><i><a class="ref" href="card_3.html#D6">CARD_3:def 6</a></i>;<br/><b>consider </b><font color="Maroon">c<sub>6</sub></font> being   <a href="ami_1.html#NM3">Instruction</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> <b> such that </b><br/><a NAME="E22:122_1_1_1_4"/><i><font color="Green">E105</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">c<sub>6</sub></font>
 <b>and </b><br/><a NAME="E23:122_1_1_1_4"/><i><font color="Green">E106</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E13:122_1_1_1_4"><i><font color="Green">E100</font></i></a></i>;<br/><b>consider </b><font color="Maroon">c<sub>7</sub></font>, <font color="Maroon">c<sub>8</sub></font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E25:122_1_1_1_4"/><i><font color="Green">E107</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K10">SubFrom</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E1:122_1_1_1_4"><i><font color="Green">E94</font></i></a>, <a class="txt" href="scmfsa10.html#E23:122_1_1_1_4"><i><font color="Green">E106</font></i></a>, <a class="ref" href="scmfsa_2.html#T56">SCMFSA_2:56</a></i>;<br/><a NAME="E26:122_1_1_1_4"/><i><font color="Green">E108</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E22:122_1_1_1_4"><i><font color="Green">E105</font></i></a>, <a class="txt" href="scmfsa10.html#E25:122_1_1_1_4"><i><font color="Green">E107</font></i></a>, <a class="ref" href="scmfsa10.html#T20" target="_self">Th20</a></i>;<br/><b>consider </b><font color="Maroon">c<sub>9</sub></font> being   <a href="ami_1.html#NM3">Instruction</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> <b> such that </b><br/><a NAME="E28:122_1_1_1_4"/><i><font color="Green">E109</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">c<sub>9</sub></font>
 <b>and </b><br/><a NAME="E29:122_1_1_1_4"/><i><font color="Green">E110</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E19:122_1_1_1_4"><i><font color="Green">E103</font></i></a></i>;<br/><b>consider </b><font color="Maroon">c<sub>10</sub></font>, <font color="Maroon">c<sub>11</sub></font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E31:122_1_1_1_4"/><i><font color="Green">E111</font></i>: 
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K10">SubFrom</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E1:122_1_1_1_4"><i><font color="Green">E94</font></i></a>, <a class="txt" href="scmfsa10.html#E29:122_1_1_1_4"><i><font color="Green">E110</font></i></a>, <a class="ref" href="scmfsa_2.html#T56">SCMFSA_2:56</a></i>;<br/><a NAME="E32:122_1_1_1_4"/><i><font color="Green">E112</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E28:122_1_1_1_4"><i><font color="Green">E109</font></i></a>, <a class="txt" href="scmfsa10.html#E31:122_1_1_1_4"><i><font color="Green">E111</font></i></a>, <a class="ref" href="scmfsa10.html#T20" target="_self">Th20</a></i>;<br/><a NAME="E33:122_1_1_1_4"/><i><font color="Green">E113</font></i>: 
 <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i><a class="ref" href="finseq_1.html#T4">FINSEQ_1:4</a>, <a class="ref" href="finseq_3.html#T29">FINSEQ_3:29</a></i>;<br/><a NAME="E34:122_1_1_1_4"/>
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span> holds <br/><span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="122_1_1_1_4_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>12</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:122_1_1_1_4_1"/><i><font color="Green">E114</font></i>: 
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span>
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_1_1_1_4_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:122_1_1_1_4_1_1"/>
( <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> 1 or <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> 2 )
 </span><b>by </b><i><a class="txt" href="scmfsa10.html#E1:122_1_1_1_4_1"><i><font color="Green">E114</font></i></a>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_1_1_1_4_1_1_1"><b>suppose </b></a><a NAME="E1:122_1_1_1_4_1_1_1"/><i><font color="Green">E115</font></i>: 
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> 1
 ;<br/><div class="add"><span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="funct_1.html#K1">.</a> 1 = 
<font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 1
<b>by </b><i><a class="txt" href="scmfsa10.html#E14:122_1_1_1_4"><i><font color="Green">E101</font></i></a>, <a class="txt" href="scmfsa10.html#E26:122_1_1_1_4"><i><font color="Green">E108</font></i></a>, <a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
;<br/><b>hence </b><a NAME="E3:122_1_1_1_4_1_1_1"/>
<span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E1:122_1_1_1_4_1_1_1"><i><font color="Green">E115</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_1_1_1_4_1_1_2"><b>suppose </b></a><a NAME="E1:122_1_1_1_4_1_1_2"/><i><font color="Green">E115</font></i>: 
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> 2
 ;<br/><div class="add"><span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="funct_1.html#K1">.</a> 2 = 
<font color="Maroon">c<sub>11</sub></font>
<b>by </b><i><a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 2
<b>by </b><i><a class="txt" href="scmfsa10.html#E20:122_1_1_1_4"><i><font color="Green">E104</font></i></a>, <a class="txt" href="scmfsa10.html#E32:122_1_1_1_4"><i><font color="Green">E112</font></i></a>, <a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
;<br/><b>hence </b><a NAME="E3:122_1_1_1_4_1_1_2"/>
<span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E1:122_1_1_1_4_1_1_2"><i><font color="Green">E115</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div><a NAME="E35:122_1_1_1_4"/><b>then </b><i><font color="Green">E114</font></i>: 
<span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E6:122_1_1_1_4"><i><font color="Green">E96</font></i></a>, <a class="txt" href="scmfsa10.html#E8:122_1_1_1_4"><i><font color="Green">E98</font></i></a>, <a class="txt" href="scmfsa10.html#E33:122_1_1_1_4"><i><font color="Green">E113</font></i></a>, <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/><a NAME="E36:122_1_1_1_4"/>
(  <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="hidden.html#R1">=</a> 3 &amp;  <a href="amistd_2.html#K4">AddressPart</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span> )
 <b>by </b><i><a class="ref" href="scmfsa10.html#T20" target="_self">Th20</a>, <a class="ref" href="scmfsa_2.html#T44">SCMFSA_2:44</a></i>;<br/><b>hence </b><a NAME="E37:122_1_1_1_4"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E1:122_1_1_1_4"><i><font color="Green">E94</font></i></a>, <a class="txt" href="scmfsa10.html#E5:122_1_1_1_4"><i><font color="Green">E95</font></i></a>, <a class="txt" href="scmfsa10.html#E35:122_1_1_1_4"><i><font color="Green">E114</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_1_1_1_5"><b>suppose </b></a><a NAME="E1:122_1_1_1_5"/><i><font color="Green">E94</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 4
 ;<br/><div class="add"><b>take </b>
 <a href="amistd_2.html#K1">PA</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
; <i><font color="Red">:: according to </font></i><a class="ref" href="amistd_2.html#D2">AMISTD_2:def 2</a><br/><b>thus </b><a NAME="E2:122_1_1_1_5"/>
 <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a>  <a href="card_3.html#K4">product</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="amistd_2.html#T9">AMISTD_2:9</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/><b>assume </b><a NAME="E3:122_1_1_1_5"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="card_3.html#K4">product</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 ;<br/><b>then consider </b><font color="Maroon">c<sub>3</sub></font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E5:122_1_1_1_5"/><i><font color="Green">E95</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>and </b><br/><a NAME="E6:122_1_1_1_5"/><i><font color="Green">E96</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E7:122_1_1_1_5"/><i><font color="Green">E97</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> holds <br/><font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="card_3.html#D5">CARD_3:def 5</a></i>;<br/><a NAME="E8:122_1_1_1_5"/><i><font color="Green">E98</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E1:122_1_1_1_5"><i><font color="Green">E94</font></i></a>, <a class="ref" href="scmfsa10.html#T34" target="_self">Th34</a></i>;<br/><a NAME="E9:122_1_1_1_5"/><b>then </b><i><font color="Green">E99</font></i>: 
1 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><a NAME="E10:122_1_1_1_5"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 1
 <b>by </b><i><a class="txt" href="scmfsa10.html#E7:122_1_1_1_5"><i><font color="Green">E97</font></i></a></i>;<br/><a NAME="E11:122_1_1_1_5"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R2">in</a>  <a href="card_3.html#K5">pi</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,1
 <b>by </b><i><a class="txt" href="scmfsa10.html#E9:122_1_1_1_5"><i><font color="Green">E99</font></i></a>, <a class="ref" href="amistd_2.html#D1">AMISTD_2:def 1</a></i>;<br/><b>then consider </b><font color="Maroon">c<sub>4</sub></font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E13:122_1_1_1_5"/><i><font color="Green">E100</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font>
 <b>and </b><br/><a NAME="E14:122_1_1_1_5"/><i><font color="Green">E101</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 1
 <b>by </b><i><a class="ref" href="card_3.html#D6">CARD_3:def 6</a></i>;<br/><a NAME="E15:122_1_1_1_5"/><i><font color="Green">E102</font></i>: 
2 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E8:122_1_1_1_5"><i><font color="Green">E98</font></i></a>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><a NAME="E16:122_1_1_1_5"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 2
 <b>by </b><i><a class="txt" href="scmfsa10.html#E7:122_1_1_1_5"><i><font color="Green">E97</font></i></a></i>;<br/><a NAME="E17:122_1_1_1_5"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R2">in</a>  <a href="card_3.html#K5">pi</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,2
 <b>by </b><i><a class="txt" href="scmfsa10.html#E15:122_1_1_1_5"><i><font color="Green">E102</font></i></a>, <a class="ref" href="amistd_2.html#D1">AMISTD_2:def 1</a></i>;<br/><b>then consider </b><font color="Maroon">c<sub>5</sub></font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E19:122_1_1_1_5"/><i><font color="Green">E103</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font>
 <b>and </b><br/><a NAME="E20:122_1_1_1_5"/><i><font color="Green">E104</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 2
 <b>by </b><i><a class="ref" href="card_3.html#D6">CARD_3:def 6</a></i>;<br/><b>consider </b><font color="Maroon">c<sub>6</sub></font> being   <a href="ami_1.html#NM3">Instruction</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> <b> such that </b><br/><a NAME="E22:122_1_1_1_5"/><i><font color="Green">E105</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">c<sub>6</sub></font>
 <b>and </b><br/><a NAME="E23:122_1_1_1_5"/><i><font color="Green">E106</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E13:122_1_1_1_5"><i><font color="Green">E100</font></i></a></i>;<br/><b>consider </b><font color="Maroon">c<sub>7</sub></font>, <font color="Maroon">c<sub>8</sub></font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E25:122_1_1_1_5"/><i><font color="Green">E107</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K11">MultBy</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E1:122_1_1_1_5"><i><font color="Green">E94</font></i></a>, <a class="txt" href="scmfsa10.html#E23:122_1_1_1_5"><i><font color="Green">E106</font></i></a>, <a class="ref" href="scmfsa_2.html#T57">SCMFSA_2:57</a></i>;<br/><a NAME="E26:122_1_1_1_5"/><i><font color="Green">E108</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E22:122_1_1_1_5"><i><font color="Green">E105</font></i></a>, <a class="txt" href="scmfsa10.html#E25:122_1_1_1_5"><i><font color="Green">E107</font></i></a>, <a class="ref" href="scmfsa10.html#T21" target="_self">Th21</a></i>;<br/><b>consider </b><font color="Maroon">c<sub>9</sub></font> being   <a href="ami_1.html#NM3">Instruction</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> <b> such that </b><br/><a NAME="E28:122_1_1_1_5"/><i><font color="Green">E109</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">c<sub>9</sub></font>
 <b>and </b><br/><a NAME="E29:122_1_1_1_5"/><i><font color="Green">E110</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E19:122_1_1_1_5"><i><font color="Green">E103</font></i></a></i>;<br/><b>consider </b><font color="Maroon">c<sub>10</sub></font>, <font color="Maroon">c<sub>11</sub></font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E31:122_1_1_1_5"/><i><font color="Green">E111</font></i>: 
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K11">MultBy</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E1:122_1_1_1_5"><i><font color="Green">E94</font></i></a>, <a class="txt" href="scmfsa10.html#E29:122_1_1_1_5"><i><font color="Green">E110</font></i></a>, <a class="ref" href="scmfsa_2.html#T57">SCMFSA_2:57</a></i>;<br/><a NAME="E32:122_1_1_1_5"/><i><font color="Green">E112</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E28:122_1_1_1_5"><i><font color="Green">E109</font></i></a>, <a class="txt" href="scmfsa10.html#E31:122_1_1_1_5"><i><font color="Green">E111</font></i></a>, <a class="ref" href="scmfsa10.html#T21" target="_self">Th21</a></i>;<br/><a NAME="E33:122_1_1_1_5"/><i><font color="Green">E113</font></i>: 
 <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i><a class="ref" href="finseq_1.html#T4">FINSEQ_1:4</a>, <a class="ref" href="finseq_3.html#T29">FINSEQ_3:29</a></i>;<br/><a NAME="E34:122_1_1_1_5"/>
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span> holds <br/><span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="122_1_1_1_5_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>12</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:122_1_1_1_5_1"/><i><font color="Green">E114</font></i>: 
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span>
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_1_1_1_5_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:122_1_1_1_5_1_1"/>
( <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> 1 or <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> 2 )
 </span><b>by </b><i><a class="txt" href="scmfsa10.html#E1:122_1_1_1_5_1"><i><font color="Green">E114</font></i></a>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_1_1_1_5_1_1_1"><b>suppose </b></a><a NAME="E1:122_1_1_1_5_1_1_1"/><i><font color="Green">E115</font></i>: 
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> 1
 ;<br/><div class="add"><span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="funct_1.html#K1">.</a> 1 = 
<font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 1
<b>by </b><i><a class="txt" href="scmfsa10.html#E14:122_1_1_1_5"><i><font color="Green">E101</font></i></a>, <a class="txt" href="scmfsa10.html#E26:122_1_1_1_5"><i><font color="Green">E108</font></i></a>, <a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
;<br/><b>hence </b><a NAME="E3:122_1_1_1_5_1_1_1"/>
<span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E1:122_1_1_1_5_1_1_1"><i><font color="Green">E115</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_1_1_1_5_1_1_2"><b>suppose </b></a><a NAME="E1:122_1_1_1_5_1_1_2"/><i><font color="Green">E115</font></i>: 
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> 2
 ;<br/><div class="add"><span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="funct_1.html#K1">.</a> 2 = 
<font color="Maroon">c<sub>11</sub></font>
<b>by </b><i><a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 2
<b>by </b><i><a class="txt" href="scmfsa10.html#E20:122_1_1_1_5"><i><font color="Green">E104</font></i></a>, <a class="txt" href="scmfsa10.html#E32:122_1_1_1_5"><i><font color="Green">E112</font></i></a>, <a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
;<br/><b>hence </b><a NAME="E3:122_1_1_1_5_1_1_2"/>
<span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E1:122_1_1_1_5_1_1_2"><i><font color="Green">E115</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div><a NAME="E35:122_1_1_1_5"/><b>then </b><i><font color="Green">E114</font></i>: 
<span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E6:122_1_1_1_5"><i><font color="Green">E96</font></i></a>, <a class="txt" href="scmfsa10.html#E8:122_1_1_1_5"><i><font color="Green">E98</font></i></a>, <a class="txt" href="scmfsa10.html#E33:122_1_1_1_5"><i><font color="Green">E113</font></i></a>, <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/><a NAME="E36:122_1_1_1_5"/>
(  <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K11">MultBy</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="hidden.html#R1">=</a> 4 &amp;  <a href="amistd_2.html#K4">AddressPart</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K11">MultBy</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span> )
 <b>by </b><i><a class="ref" href="scmfsa10.html#T21" target="_self">Th21</a>, <a class="ref" href="scmfsa_2.html#T45">SCMFSA_2:45</a></i>;<br/><b>hence </b><a NAME="E37:122_1_1_1_5"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E1:122_1_1_1_5"><i><font color="Green">E94</font></i></a>, <a class="txt" href="scmfsa10.html#E5:122_1_1_1_5"><i><font color="Green">E95</font></i></a>, <a class="txt" href="scmfsa10.html#E35:122_1_1_1_5"><i><font color="Green">E114</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_1_1_1_6"><b>suppose </b></a><a NAME="E1:122_1_1_1_6"/><i><font color="Green">E94</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 5
 ;<br/><div class="add"><b>take </b>
 <a href="amistd_2.html#K1">PA</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
; <i><font color="Red">:: according to </font></i><a class="ref" href="amistd_2.html#D2">AMISTD_2:def 2</a><br/><b>thus </b><a NAME="E2:122_1_1_1_6"/>
 <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a>  <a href="card_3.html#K4">product</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="amistd_2.html#T9">AMISTD_2:9</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/><b>assume </b><a NAME="E3:122_1_1_1_6"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="card_3.html#K4">product</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 ;<br/><b>then consider </b><font color="Maroon">c<sub>3</sub></font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E5:122_1_1_1_6"/><i><font color="Green">E95</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>and </b><br/><a NAME="E6:122_1_1_1_6"/><i><font color="Green">E96</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E7:122_1_1_1_6"/><i><font color="Green">E97</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> holds <br/><font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="card_3.html#D5">CARD_3:def 5</a></i>;<br/><a NAME="E8:122_1_1_1_6"/><i><font color="Green">E98</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E1:122_1_1_1_6"><i><font color="Green">E94</font></i></a>, <a class="ref" href="scmfsa10.html#T35" target="_self">Th35</a></i>;<br/><a NAME="E9:122_1_1_1_6"/><b>then </b><i><font color="Green">E99</font></i>: 
1 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><a NAME="E10:122_1_1_1_6"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 1
 <b>by </b><i><a class="txt" href="scmfsa10.html#E7:122_1_1_1_6"><i><font color="Green">E97</font></i></a></i>;<br/><a NAME="E11:122_1_1_1_6"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R2">in</a>  <a href="card_3.html#K5">pi</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,1
 <b>by </b><i><a class="txt" href="scmfsa10.html#E9:122_1_1_1_6"><i><font color="Green">E99</font></i></a>, <a class="ref" href="amistd_2.html#D1">AMISTD_2:def 1</a></i>;<br/><b>then consider </b><font color="Maroon">c<sub>4</sub></font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E13:122_1_1_1_6"/><i><font color="Green">E100</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font>
 <b>and </b><br/><a NAME="E14:122_1_1_1_6"/><i><font color="Green">E101</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 1
 <b>by </b><i><a class="ref" href="card_3.html#D6">CARD_3:def 6</a></i>;<br/><a NAME="E15:122_1_1_1_6"/><i><font color="Green">E102</font></i>: 
2 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E8:122_1_1_1_6"><i><font color="Green">E98</font></i></a>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><a NAME="E16:122_1_1_1_6"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 2
 <b>by </b><i><a class="txt" href="scmfsa10.html#E7:122_1_1_1_6"><i><font color="Green">E97</font></i></a></i>;<br/><a NAME="E17:122_1_1_1_6"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R2">in</a>  <a href="card_3.html#K5">pi</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,2
 <b>by </b><i><a class="txt" href="scmfsa10.html#E15:122_1_1_1_6"><i><font color="Green">E102</font></i></a>, <a class="ref" href="amistd_2.html#D1">AMISTD_2:def 1</a></i>;<br/><b>then consider </b><font color="Maroon">c<sub>5</sub></font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E19:122_1_1_1_6"/><i><font color="Green">E103</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font>
 <b>and </b><br/><a NAME="E20:122_1_1_1_6"/><i><font color="Green">E104</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 2
 <b>by </b><i><a class="ref" href="card_3.html#D6">CARD_3:def 6</a></i>;<br/><b>consider </b><font color="Maroon">c<sub>6</sub></font> being   <a href="ami_1.html#NM3">Instruction</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> <b> such that </b><br/><a NAME="E22:122_1_1_1_6"/><i><font color="Green">E105</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">c<sub>6</sub></font>
 <b>and </b><br/><a NAME="E23:122_1_1_1_6"/><i><font color="Green">E106</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E13:122_1_1_1_6"><i><font color="Green">E100</font></i></a></i>;<br/><b>consider </b><font color="Maroon">c<sub>7</sub></font>, <font color="Maroon">c<sub>8</sub></font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E25:122_1_1_1_6"/><i><font color="Green">E107</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K12">Divide</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E1:122_1_1_1_6"><i><font color="Green">E94</font></i></a>, <a class="txt" href="scmfsa10.html#E23:122_1_1_1_6"><i><font color="Green">E106</font></i></a>, <a class="ref" href="scmfsa_2.html#T58">SCMFSA_2:58</a></i>;<br/><a NAME="E26:122_1_1_1_6"/><i><font color="Green">E108</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E22:122_1_1_1_6"><i><font color="Green">E105</font></i></a>, <a class="txt" href="scmfsa10.html#E25:122_1_1_1_6"><i><font color="Green">E107</font></i></a>, <a class="ref" href="scmfsa10.html#T22" target="_self">Th22</a></i>;<br/><b>consider </b><font color="Maroon">c<sub>9</sub></font> being   <a href="ami_1.html#NM3">Instruction</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> <b> such that </b><br/><a NAME="E28:122_1_1_1_6"/><i><font color="Green">E109</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">c<sub>9</sub></font>
 <b>and </b><br/><a NAME="E29:122_1_1_1_6"/><i><font color="Green">E110</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E19:122_1_1_1_6"><i><font color="Green">E103</font></i></a></i>;<br/><b>consider </b><font color="Maroon">c<sub>10</sub></font>, <font color="Maroon">c<sub>11</sub></font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E31:122_1_1_1_6"/><i><font color="Green">E111</font></i>: 
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K12">Divide</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E1:122_1_1_1_6"><i><font color="Green">E94</font></i></a>, <a class="txt" href="scmfsa10.html#E29:122_1_1_1_6"><i><font color="Green">E110</font></i></a>, <a class="ref" href="scmfsa_2.html#T58">SCMFSA_2:58</a></i>;<br/><a NAME="E32:122_1_1_1_6"/><i><font color="Green">E112</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E28:122_1_1_1_6"><i><font color="Green">E109</font></i></a>, <a class="txt" href="scmfsa10.html#E31:122_1_1_1_6"><i><font color="Green">E111</font></i></a>, <a class="ref" href="scmfsa10.html#T22" target="_self">Th22</a></i>;<br/><a NAME="E33:122_1_1_1_6"/><i><font color="Green">E113</font></i>: 
 <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i><a class="ref" href="finseq_1.html#T4">FINSEQ_1:4</a>, <a class="ref" href="finseq_3.html#T29">FINSEQ_3:29</a></i>;<br/><a NAME="E34:122_1_1_1_6"/>
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span> holds <br/><span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="122_1_1_1_6_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>12</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:122_1_1_1_6_1"/><i><font color="Green">E114</font></i>: 
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span>
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_1_1_1_6_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:122_1_1_1_6_1_1"/>
( <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> 1 or <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> 2 )
 </span><b>by </b><i><a class="txt" href="scmfsa10.html#E1:122_1_1_1_6_1"><i><font color="Green">E114</font></i></a>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_1_1_1_6_1_1_1"><b>suppose </b></a><a NAME="E1:122_1_1_1_6_1_1_1"/><i><font color="Green">E115</font></i>: 
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> 1
 ;<br/><div class="add"><span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="funct_1.html#K1">.</a> 1 = 
<font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 1
<b>by </b><i><a class="txt" href="scmfsa10.html#E14:122_1_1_1_6"><i><font color="Green">E101</font></i></a>, <a class="txt" href="scmfsa10.html#E26:122_1_1_1_6"><i><font color="Green">E108</font></i></a>, <a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
;<br/><b>hence </b><a NAME="E3:122_1_1_1_6_1_1_1"/>
<span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E1:122_1_1_1_6_1_1_1"><i><font color="Green">E115</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_1_1_1_6_1_1_2"><b>suppose </b></a><a NAME="E1:122_1_1_1_6_1_1_2"/><i><font color="Green">E115</font></i>: 
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> 2
 ;<br/><div class="add"><span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="funct_1.html#K1">.</a> 2 = 
<font color="Maroon">c<sub>11</sub></font>
<b>by </b><i><a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 2
<b>by </b><i><a class="txt" href="scmfsa10.html#E20:122_1_1_1_6"><i><font color="Green">E104</font></i></a>, <a class="txt" href="scmfsa10.html#E32:122_1_1_1_6"><i><font color="Green">E112</font></i></a>, <a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
;<br/><b>hence </b><a NAME="E3:122_1_1_1_6_1_1_2"/>
<span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E1:122_1_1_1_6_1_1_2"><i><font color="Green">E115</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div><a NAME="E35:122_1_1_1_6"/><b>then </b><i><font color="Green">E114</font></i>: 
<span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E6:122_1_1_1_6"><i><font color="Green">E96</font></i></a>, <a class="txt" href="scmfsa10.html#E8:122_1_1_1_6"><i><font color="Green">E98</font></i></a>, <a class="txt" href="scmfsa10.html#E33:122_1_1_1_6"><i><font color="Green">E113</font></i></a>, <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/><a NAME="E36:122_1_1_1_6"/>
(  <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K12">Divide</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="hidden.html#R1">=</a> 5 &amp;  <a href="amistd_2.html#K4">AddressPart</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K12">Divide</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span> )
 <b>by </b><i><a class="ref" href="scmfsa10.html#T22" target="_self">Th22</a>, <a class="ref" href="scmfsa_2.html#T46">SCMFSA_2:46</a></i>;<br/><b>hence </b><a NAME="E37:122_1_1_1_6"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E1:122_1_1_1_6"><i><font color="Green">E94</font></i></a>, <a class="txt" href="scmfsa10.html#E5:122_1_1_1_6"><i><font color="Green">E95</font></i></a>, <a class="txt" href="scmfsa10.html#E35:122_1_1_1_6"><i><font color="Green">E114</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_1_1_1_7"><b>suppose </b></a><a NAME="E1:122_1_1_1_7"/><i><font color="Green">E94</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 6
 ;<br/><div class="add"><b>take </b>
 <a href="amistd_2.html#K1">PA</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
; <i><font color="Red">:: according to </font></i><a class="ref" href="amistd_2.html#D2">AMISTD_2:def 2</a><br/><b>thus </b><a NAME="E2:122_1_1_1_7"/>
 <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a>  <a href="card_3.html#K4">product</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="amistd_2.html#T9">AMISTD_2:9</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/><b>assume </b><a NAME="E3:122_1_1_1_7"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="card_3.html#K4">product</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 ;<br/><b>then consider </b><font color="Maroon">c<sub>3</sub></font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E5:122_1_1_1_7"/><i><font color="Green">E95</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>and </b><br/><a NAME="E6:122_1_1_1_7"/><i><font color="Green">E96</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E7:122_1_1_1_7"/><i><font color="Green">E97</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> holds <br/><font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="card_3.html#D5">CARD_3:def 5</a></i>;<br/><a NAME="E8:122_1_1_1_7"/><i><font color="Green">E98</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default">1</span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E1:122_1_1_1_7"><i><font color="Green">E94</font></i></a>, <a class="ref" href="scmfsa10.html#T36" target="_self">Th36</a></i>;<br/><a NAME="E9:122_1_1_1_7"/><b>then </b><i><font color="Green">E99</font></i>: 
1 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><a NAME="E10:122_1_1_1_7"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 1
 <b>by </b><i><a class="txt" href="scmfsa10.html#E7:122_1_1_1_7"><i><font color="Green">E97</font></i></a></i>;<br/><a NAME="E11:122_1_1_1_7"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R2">in</a>  <a href="card_3.html#K5">pi</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,1
 <b>by </b><i><a class="txt" href="scmfsa10.html#E9:122_1_1_1_7"><i><font color="Green">E99</font></i></a>, <a class="ref" href="amistd_2.html#D1">AMISTD_2:def 1</a></i>;<br/><b>then consider </b><font color="Maroon">c<sub>4</sub></font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E13:122_1_1_1_7"/><i><font color="Green">E100</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font>
 <b>and </b><br/><a NAME="E14:122_1_1_1_7"/><i><font color="Green">E101</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 1
 <b>by </b><i><a class="ref" href="card_3.html#D6">CARD_3:def 6</a></i>;<br/><b>consider </b><font color="Maroon">c<sub>5</sub></font> being   <a href="ami_1.html#NM3">Instruction</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> <b> such that </b><br/><a NAME="E16:122_1_1_1_7"/><i><font color="Green">E102</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">c<sub>5</sub></font>
 <b>and </b><br/><a NAME="E17:122_1_1_1_7"/><i><font color="Green">E103</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E13:122_1_1_1_7"><i><font color="Green">E100</font></i></a></i>;<br/><b>consider </b><font color="Maroon">c<sub>6</sub></font> being   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> <b> such that </b><br/><a NAME="E19:122_1_1_1_7"/><i><font color="Green">E104</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K13">goto</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E1:122_1_1_1_7"><i><font color="Green">E94</font></i></a>, <a class="txt" href="scmfsa10.html#E17:122_1_1_1_7"><i><font color="Green">E103</font></i></a>, <a class="ref" href="scmfsa_2.html#T59">SCMFSA_2:59</a></i>;<br/><a NAME="E20:122_1_1_1_7"/><i><font color="Green">E105</font></i>: 
 <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">c<sub>6</sub></font></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default">1</span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="finseq_1.html#T4">FINSEQ_1:4</a>, <a class="ref" href="finseq_1.html#D8">FINSEQ_1:def 8</a></i>;<br/><a NAME="E21:122_1_1_1_7"/>
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default">1</span><a href="tarski.html#K1">}</a></span> holds <br/><span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">c<sub>6</sub></font></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="122_1_1_1_7_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>7</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:122_1_1_1_7_1"/>
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default">1</span><a href="tarski.html#K1">}</a></span>
 ;<br/>

<a NAME="E2:122_1_1_1_7_1"/><b>then </b>
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> 1
 
<b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<b>hence </b><a NAME="E3:122_1_1_1_7_1"/>
<span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">c<sub>6</sub></font></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E14:122_1_1_1_7"><i><font color="Green">E101</font></i></a>, <a class="txt" href="scmfsa10.html#E16:122_1_1_1_7"><i><font color="Green">E102</font></i></a>, <a class="txt" href="scmfsa10.html#E19:122_1_1_1_7"><i><font color="Green">E104</font></i></a>, <a class="ref" href="scmfsa10.html#T23" target="_self">Th23</a></i>;<br/>


</div><b>end;</b></div><a NAME="E22:122_1_1_1_7"/><b>then </b><i><font color="Green">E106</font></i>: 
<span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">c<sub>6</sub></font></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E6:122_1_1_1_7"><i><font color="Green">E96</font></i></a>, <a class="txt" href="scmfsa10.html#E8:122_1_1_1_7"><i><font color="Green">E98</font></i></a>, <a class="txt" href="scmfsa10.html#E20:122_1_1_1_7"><i><font color="Green">E105</font></i></a>, <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/><a NAME="E23:122_1_1_1_7"/>
(  <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K13">goto</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="hidden.html#R1">=</a> 6 &amp;  <a href="amistd_2.html#K4">AddressPart</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K13">goto</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">c<sub>6</sub></font></span><a href="finseq_1.html#K12">*&gt;</a></span> )
 <b>by </b><i><a class="ref" href="scmfsa10.html#T23" target="_self">Th23</a>, <a class="ref" href="scmfsa_2.html#T47">SCMFSA_2:47</a></i>;<br/><b>hence </b><a NAME="E24:122_1_1_1_7"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E1:122_1_1_1_7"><i><font color="Green">E94</font></i></a>, <a class="txt" href="scmfsa10.html#E5:122_1_1_1_7"><i><font color="Green">E95</font></i></a>, <a class="txt" href="scmfsa10.html#E22:122_1_1_1_7"><i><font color="Green">E106</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_1_1_1_8"><b>suppose </b></a><a NAME="E1:122_1_1_1_8"/><i><font color="Green">E94</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 7
 ;<br/><div class="add"><b>take </b>
 <a href="amistd_2.html#K1">PA</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
; <i><font color="Red">:: according to </font></i><a class="ref" href="amistd_2.html#D2">AMISTD_2:def 2</a><br/><b>thus </b><a NAME="E2:122_1_1_1_8"/>
 <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a>  <a href="card_3.html#K4">product</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="amistd_2.html#T9">AMISTD_2:9</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/><b>assume </b><a NAME="E3:122_1_1_1_8"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="card_3.html#K4">product</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 ;<br/><b>then consider </b><font color="Maroon">c<sub>3</sub></font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E5:122_1_1_1_8"/><i><font color="Green">E95</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>and </b><br/><a NAME="E6:122_1_1_1_8"/><i><font color="Green">E96</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E7:122_1_1_1_8"/><i><font color="Green">E97</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> holds <br/><font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="card_3.html#D5">CARD_3:def 5</a></i>;<br/><a NAME="E8:122_1_1_1_8"/><i><font color="Green">E98</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E1:122_1_1_1_8"><i><font color="Green">E94</font></i></a>, <a class="ref" href="scmfsa10.html#T37" target="_self">Th37</a></i>;<br/><a NAME="E9:122_1_1_1_8"/><b>then </b><i><font color="Green">E99</font></i>: 
1 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><a NAME="E10:122_1_1_1_8"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 1
 <b>by </b><i><a class="txt" href="scmfsa10.html#E7:122_1_1_1_8"><i><font color="Green">E97</font></i></a></i>;<br/><a NAME="E11:122_1_1_1_8"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R2">in</a>  <a href="card_3.html#K5">pi</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,1
 <b>by </b><i><a class="txt" href="scmfsa10.html#E9:122_1_1_1_8"><i><font color="Green">E99</font></i></a>, <a class="ref" href="amistd_2.html#D1">AMISTD_2:def 1</a></i>;<br/><b>then consider </b><font color="Maroon">c<sub>4</sub></font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E13:122_1_1_1_8"/><i><font color="Green">E100</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font>
 <b>and </b><br/><a NAME="E14:122_1_1_1_8"/><i><font color="Green">E101</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 1
 <b>by </b><i><a class="ref" href="card_3.html#D6">CARD_3:def 6</a></i>;<br/><a NAME="E15:122_1_1_1_8"/><i><font color="Green">E102</font></i>: 
2 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E8:122_1_1_1_8"><i><font color="Green">E98</font></i></a>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><a NAME="E16:122_1_1_1_8"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 2
 <b>by </b><i><a class="txt" href="scmfsa10.html#E7:122_1_1_1_8"><i><font color="Green">E97</font></i></a></i>;<br/><a NAME="E17:122_1_1_1_8"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R2">in</a>  <a href="card_3.html#K5">pi</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,2
 <b>by </b><i><a class="txt" href="scmfsa10.html#E15:122_1_1_1_8"><i><font color="Green">E102</font></i></a>, <a class="ref" href="amistd_2.html#D1">AMISTD_2:def 1</a></i>;<br/><b>then consider </b><font color="Maroon">c<sub>5</sub></font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E19:122_1_1_1_8"/><i><font color="Green">E103</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font>
 <b>and </b><br/><a NAME="E20:122_1_1_1_8"/><i><font color="Green">E104</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 2
 <b>by </b><i><a class="ref" href="card_3.html#D6">CARD_3:def 6</a></i>;<br/><b>consider </b><font color="Maroon">c<sub>6</sub></font> being   <a href="ami_1.html#NM3">Instruction</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> <b> such that </b><br/><a NAME="E22:122_1_1_1_8"/><i><font color="Green">E105</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">c<sub>6</sub></font>
 <b>and </b><br/><a NAME="E23:122_1_1_1_8"/><i><font color="Green">E106</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E13:122_1_1_1_8"><i><font color="Green">E100</font></i></a></i>;<br/><b>consider </b><font color="Maroon">c<sub>7</sub></font> being   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> , <font color="Maroon">c<sub>8</sub></font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E25:122_1_1_1_8"/><i><font color="Green">E107</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> <a href="scmfsa_2.html#K14">=0_goto</a> <font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E1:122_1_1_1_8"><i><font color="Green">E94</font></i></a>, <a class="txt" href="scmfsa10.html#E23:122_1_1_1_8"><i><font color="Green">E106</font></i></a>, <a class="ref" href="scmfsa_2.html#T60">SCMFSA_2:60</a></i>;<br/><a NAME="E26:122_1_1_1_8"/><i><font color="Green">E108</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E22:122_1_1_1_8"><i><font color="Green">E105</font></i></a>, <a class="txt" href="scmfsa10.html#E25:122_1_1_1_8"><i><font color="Green">E107</font></i></a>, <a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a></i>;<br/><b>consider </b><font color="Maroon">c<sub>9</sub></font> being   <a href="ami_1.html#NM3">Instruction</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> <b> such that </b><br/><a NAME="E28:122_1_1_1_8"/><i><font color="Green">E109</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">c<sub>9</sub></font>
 <b>and </b><br/><a NAME="E29:122_1_1_1_8"/><i><font color="Green">E110</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E19:122_1_1_1_8"><i><font color="Green">E103</font></i></a></i>;<br/><b>consider </b><font color="Maroon">c<sub>10</sub></font> being   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> , <font color="Maroon">c<sub>11</sub></font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E31:122_1_1_1_8"/><i><font color="Green">E111</font></i>: 
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>11</sub></font> <a href="scmfsa_2.html#K14">=0_goto</a> <font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E1:122_1_1_1_8"><i><font color="Green">E94</font></i></a>, <a class="txt" href="scmfsa10.html#E29:122_1_1_1_8"><i><font color="Green">E110</font></i></a>, <a class="ref" href="scmfsa_2.html#T60">SCMFSA_2:60</a></i>;<br/><a NAME="E32:122_1_1_1_8"/><i><font color="Green">E112</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E28:122_1_1_1_8"><i><font color="Green">E109</font></i></a>, <a class="txt" href="scmfsa10.html#E31:122_1_1_1_8"><i><font color="Green">E111</font></i></a>, <a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a></i>;<br/><a NAME="E33:122_1_1_1_8"/><i><font color="Green">E113</font></i>: 
 <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i><a class="ref" href="finseq_1.html#T4">FINSEQ_1:4</a>, <a class="ref" href="finseq_3.html#T29">FINSEQ_3:29</a></i>;<br/><a NAME="E34:122_1_1_1_8"/>
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span> holds <br/><span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="122_1_1_1_8_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>12</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:122_1_1_1_8_1"/><i><font color="Green">E114</font></i>: 
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span>
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_1_1_1_8_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:122_1_1_1_8_1_1"/>
( <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> 1 or <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> 2 )
 </span><b>by </b><i><a class="txt" href="scmfsa10.html#E1:122_1_1_1_8_1"><i><font color="Green">E114</font></i></a>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_1_1_1_8_1_1_1"><b>suppose </b></a><a NAME="E1:122_1_1_1_8_1_1_1"/><i><font color="Green">E115</font></i>: 
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> 1
 ;<br/><div class="add"><span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="funct_1.html#K1">.</a> 1 = 
<font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 1
<b>by </b><i><a class="txt" href="scmfsa10.html#E14:122_1_1_1_8"><i><font color="Green">E101</font></i></a>, <a class="txt" href="scmfsa10.html#E26:122_1_1_1_8"><i><font color="Green">E108</font></i></a>, <a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
;<br/><b>hence </b><a NAME="E3:122_1_1_1_8_1_1_1"/>
<span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E1:122_1_1_1_8_1_1_1"><i><font color="Green">E115</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_1_1_1_8_1_1_2"><b>suppose </b></a><a NAME="E1:122_1_1_1_8_1_1_2"/><i><font color="Green">E115</font></i>: 
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> 2
 ;<br/><div class="add"><span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="funct_1.html#K1">.</a> 2 = 
<font color="Maroon">c<sub>11</sub></font>
<b>by </b><i><a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 2
<b>by </b><i><a class="txt" href="scmfsa10.html#E20:122_1_1_1_8"><i><font color="Green">E104</font></i></a>, <a class="txt" href="scmfsa10.html#E32:122_1_1_1_8"><i><font color="Green">E112</font></i></a>, <a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
;<br/><b>hence </b><a NAME="E3:122_1_1_1_8_1_1_2"/>
<span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E1:122_1_1_1_8_1_1_2"><i><font color="Green">E115</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div><a NAME="E35:122_1_1_1_8"/><b>then </b><i><font color="Green">E114</font></i>: 
<span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E6:122_1_1_1_8"><i><font color="Green">E96</font></i></a>, <a class="txt" href="scmfsa10.html#E8:122_1_1_1_8"><i><font color="Green">E98</font></i></a>, <a class="txt" href="scmfsa10.html#E33:122_1_1_1_8"><i><font color="Green">E113</font></i></a>, <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/><a NAME="E36:122_1_1_1_8"/>
(  <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="scmfsa_2.html#K14">=0_goto</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="hidden.html#R1">=</a> 7 &amp;  <a href="amistd_2.html#K4">AddressPart</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="scmfsa_2.html#K14">=0_goto</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span> )
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, <a class="ref" href="scmfsa_2.html#T48">SCMFSA_2:48</a></i>;<br/><b>hence </b><a NAME="E37:122_1_1_1_8"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E1:122_1_1_1_8"><i><font color="Green">E94</font></i></a>, <a class="txt" href="scmfsa10.html#E5:122_1_1_1_8"><i><font color="Green">E95</font></i></a>, <a class="txt" href="scmfsa10.html#E35:122_1_1_1_8"><i><font color="Green">E114</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_1_1_1_9"><b>suppose </b></a><a NAME="E1:122_1_1_1_9"/><i><font color="Green">E94</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 8
 ;<br/><div class="add"><b>take </b>
 <a href="amistd_2.html#K1">PA</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
; <i><font color="Red">:: according to </font></i><a class="ref" href="amistd_2.html#D2">AMISTD_2:def 2</a><br/><b>thus </b><a NAME="E2:122_1_1_1_9"/>
 <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a>  <a href="card_3.html#K4">product</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="amistd_2.html#T9">AMISTD_2:9</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/><b>assume </b><a NAME="E3:122_1_1_1_9"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="card_3.html#K4">product</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 ;<br/><b>then consider </b><font color="Maroon">c<sub>3</sub></font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E5:122_1_1_1_9"/><i><font color="Green">E95</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>and </b><br/><a NAME="E6:122_1_1_1_9"/><i><font color="Green">E96</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E7:122_1_1_1_9"/><i><font color="Green">E97</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> holds <br/><font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="card_3.html#D5">CARD_3:def 5</a></i>;<br/><a NAME="E8:122_1_1_1_9"/><i><font color="Green">E98</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E1:122_1_1_1_9"><i><font color="Green">E94</font></i></a>, <a class="ref" href="scmfsa10.html#T38" target="_self">Th38</a></i>;<br/><a NAME="E9:122_1_1_1_9"/><b>then </b><i><font color="Green">E99</font></i>: 
1 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><a NAME="E10:122_1_1_1_9"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 1
 <b>by </b><i><a class="txt" href="scmfsa10.html#E7:122_1_1_1_9"><i><font color="Green">E97</font></i></a></i>;<br/><a NAME="E11:122_1_1_1_9"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R2">in</a>  <a href="card_3.html#K5">pi</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,1
 <b>by </b><i><a class="txt" href="scmfsa10.html#E9:122_1_1_1_9"><i><font color="Green">E99</font></i></a>, <a class="ref" href="amistd_2.html#D1">AMISTD_2:def 1</a></i>;<br/><b>then consider </b><font color="Maroon">c<sub>4</sub></font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E13:122_1_1_1_9"/><i><font color="Green">E100</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font>
 <b>and </b><br/><a NAME="E14:122_1_1_1_9"/><i><font color="Green">E101</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 1
 <b>by </b><i><a class="ref" href="card_3.html#D6">CARD_3:def 6</a></i>;<br/><a NAME="E15:122_1_1_1_9"/><i><font color="Green">E102</font></i>: 
2 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E8:122_1_1_1_9"><i><font color="Green">E98</font></i></a>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><a NAME="E16:122_1_1_1_9"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 2
 <b>by </b><i><a class="txt" href="scmfsa10.html#E7:122_1_1_1_9"><i><font color="Green">E97</font></i></a></i>;<br/><a NAME="E17:122_1_1_1_9"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R2">in</a>  <a href="card_3.html#K5">pi</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,2
 <b>by </b><i><a class="txt" href="scmfsa10.html#E15:122_1_1_1_9"><i><font color="Green">E102</font></i></a>, <a class="ref" href="amistd_2.html#D1">AMISTD_2:def 1</a></i>;<br/><b>then consider </b><font color="Maroon">c<sub>5</sub></font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E19:122_1_1_1_9"/><i><font color="Green">E103</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font>
 <b>and </b><br/><a NAME="E20:122_1_1_1_9"/><i><font color="Green">E104</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 2
 <b>by </b><i><a class="ref" href="card_3.html#D6">CARD_3:def 6</a></i>;<br/><b>consider </b><font color="Maroon">c<sub>6</sub></font> being   <a href="ami_1.html#NM3">Instruction</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> <b> such that </b><br/><a NAME="E22:122_1_1_1_9"/><i><font color="Green">E105</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">c<sub>6</sub></font>
 <b>and </b><br/><a NAME="E23:122_1_1_1_9"/><i><font color="Green">E106</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E13:122_1_1_1_9"><i><font color="Green">E100</font></i></a></i>;<br/><b>consider </b><font color="Maroon">c<sub>7</sub></font> being   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> , <font color="Maroon">c<sub>8</sub></font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E25:122_1_1_1_9"/><i><font color="Green">E107</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> <a href="scmfsa_2.html#K15">&gt;0_goto</a> <font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E1:122_1_1_1_9"><i><font color="Green">E94</font></i></a>, <a class="txt" href="scmfsa10.html#E23:122_1_1_1_9"><i><font color="Green">E106</font></i></a>, <a class="ref" href="scmfsa_2.html#T61">SCMFSA_2:61</a></i>;<br/><a NAME="E26:122_1_1_1_9"/><i><font color="Green">E108</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E22:122_1_1_1_9"><i><font color="Green">E105</font></i></a>, <a class="txt" href="scmfsa10.html#E25:122_1_1_1_9"><i><font color="Green">E107</font></i></a>, <a class="ref" href="scmfsa10.html#T25" target="_self">Th25</a></i>;<br/><b>consider </b><font color="Maroon">c<sub>9</sub></font> being   <a href="ami_1.html#NM3">Instruction</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> <b> such that </b><br/><a NAME="E28:122_1_1_1_9"/><i><font color="Green">E109</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">c<sub>9</sub></font>
 <b>and </b><br/><a NAME="E29:122_1_1_1_9"/><i><font color="Green">E110</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E19:122_1_1_1_9"><i><font color="Green">E103</font></i></a></i>;<br/><b>consider </b><font color="Maroon">c<sub>10</sub></font> being   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> , <font color="Maroon">c<sub>11</sub></font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E31:122_1_1_1_9"/><i><font color="Green">E111</font></i>: 
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>11</sub></font> <a href="scmfsa_2.html#K15">&gt;0_goto</a> <font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E1:122_1_1_1_9"><i><font color="Green">E94</font></i></a>, <a class="txt" href="scmfsa10.html#E29:122_1_1_1_9"><i><font color="Green">E110</font></i></a>, <a class="ref" href="scmfsa_2.html#T61">SCMFSA_2:61</a></i>;<br/><a NAME="E32:122_1_1_1_9"/><i><font color="Green">E112</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E28:122_1_1_1_9"><i><font color="Green">E109</font></i></a>, <a class="txt" href="scmfsa10.html#E31:122_1_1_1_9"><i><font color="Green">E111</font></i></a>, <a class="ref" href="scmfsa10.html#T25" target="_self">Th25</a></i>;<br/><a NAME="E33:122_1_1_1_9"/><i><font color="Green">E113</font></i>: 
 <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i><a class="ref" href="finseq_1.html#T4">FINSEQ_1:4</a>, <a class="ref" href="finseq_3.html#T29">FINSEQ_3:29</a></i>;<br/><a NAME="E34:122_1_1_1_9"/>
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span> holds <br/><span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="122_1_1_1_9_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>12</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:122_1_1_1_9_1"/><i><font color="Green">E114</font></i>: 
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span>
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_1_1_1_9_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:122_1_1_1_9_1_1"/>
( <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> 1 or <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> 2 )
 </span><b>by </b><i><a class="txt" href="scmfsa10.html#E1:122_1_1_1_9_1"><i><font color="Green">E114</font></i></a>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_1_1_1_9_1_1_1"><b>suppose </b></a><a NAME="E1:122_1_1_1_9_1_1_1"/><i><font color="Green">E115</font></i>: 
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> 1
 ;<br/><div class="add"><span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="funct_1.html#K1">.</a> 1 = 
<font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 1
<b>by </b><i><a class="txt" href="scmfsa10.html#E14:122_1_1_1_9"><i><font color="Green">E101</font></i></a>, <a class="txt" href="scmfsa10.html#E26:122_1_1_1_9"><i><font color="Green">E108</font></i></a>, <a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
;<br/><b>hence </b><a NAME="E3:122_1_1_1_9_1_1_1"/>
<span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E1:122_1_1_1_9_1_1_1"><i><font color="Green">E115</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_1_1_1_9_1_1_2"><b>suppose </b></a><a NAME="E1:122_1_1_1_9_1_1_2"/><i><font color="Green">E115</font></i>: 
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> 2
 ;<br/><div class="add"><span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="funct_1.html#K1">.</a> 2 = 
<font color="Maroon">c<sub>11</sub></font>
<b>by </b><i><a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 2
<b>by </b><i><a class="txt" href="scmfsa10.html#E20:122_1_1_1_9"><i><font color="Green">E104</font></i></a>, <a class="txt" href="scmfsa10.html#E32:122_1_1_1_9"><i><font color="Green">E112</font></i></a>, <a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
;<br/><b>hence </b><a NAME="E3:122_1_1_1_9_1_1_2"/>
<span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E1:122_1_1_1_9_1_1_2"><i><font color="Green">E115</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div><a NAME="E35:122_1_1_1_9"/><b>then </b><i><font color="Green">E114</font></i>: 
<span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E6:122_1_1_1_9"><i><font color="Green">E96</font></i></a>, <a class="txt" href="scmfsa10.html#E8:122_1_1_1_9"><i><font color="Green">E98</font></i></a>, <a class="txt" href="scmfsa10.html#E33:122_1_1_1_9"><i><font color="Green">E113</font></i></a>, <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/><a NAME="E36:122_1_1_1_9"/>
(  <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="scmfsa_2.html#K15">&gt;0_goto</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="hidden.html#R1">=</a> 8 &amp;  <a href="amistd_2.html#K4">AddressPart</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="scmfsa_2.html#K15">&gt;0_goto</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span> )
 <b>by </b><i><a class="ref" href="scmfsa10.html#T25" target="_self">Th25</a>, <a class="ref" href="scmfsa_2.html#T49">SCMFSA_2:49</a></i>;<br/><b>hence </b><a NAME="E37:122_1_1_1_9"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E1:122_1_1_1_9"><i><font color="Green">E94</font></i></a>, <a class="txt" href="scmfsa10.html#E5:122_1_1_1_9"><i><font color="Green">E95</font></i></a>, <a class="txt" href="scmfsa10.html#E35:122_1_1_1_9"><i><font color="Green">E114</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_1_1_1_10"><b>suppose </b></a><a NAME="E1:122_1_1_1_10"/><i><font color="Green">E94</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 9
 ;<br/><div class="add"><b>take </b>
 <a href="amistd_2.html#K1">PA</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
; <i><font color="Red">:: according to </font></i><a class="ref" href="amistd_2.html#D2">AMISTD_2:def 2</a><br/><b>thus </b><a NAME="E2:122_1_1_1_10"/>
 <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a>  <a href="card_3.html#K4">product</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="amistd_2.html#T9">AMISTD_2:9</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/><b>assume </b><a NAME="E3:122_1_1_1_10"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="card_3.html#K4">product</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 ;<br/><b>then consider </b><font color="Maroon">c<sub>3</sub></font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E5:122_1_1_1_10"/><i><font color="Green">E95</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>and </b><br/><a NAME="E6:122_1_1_1_10"/><i><font color="Green">E96</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E7:122_1_1_1_10"/><i><font color="Green">E97</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> holds <br/><font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="card_3.html#D5">CARD_3:def 5</a></i>;<br/><a NAME="E8:122_1_1_1_10"/><i><font color="Green">E98</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="enumset1.html#K1">{</a><span class="default">1,2,3</span><a href="enumset1.html#K1">}</a></span>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E1:122_1_1_1_10"><i><font color="Green">E94</font></i></a>, <a class="ref" href="scmfsa10.html#T39" target="_self">Th39</a></i>;<br/><a NAME="E9:122_1_1_1_10"/><b>then </b><i><font color="Green">E99</font></i>: 
1 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="enumset1.html#D1">ENUMSET1:def 1</a></i>;<br/><a NAME="E10:122_1_1_1_10"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 1
 <b>by </b><i><a class="txt" href="scmfsa10.html#E7:122_1_1_1_10"><i><font color="Green">E97</font></i></a></i>;<br/><a NAME="E11:122_1_1_1_10"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R2">in</a>  <a href="card_3.html#K5">pi</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,1
 <b>by </b><i><a class="txt" href="scmfsa10.html#E9:122_1_1_1_10"><i><font color="Green">E99</font></i></a>, <a class="ref" href="amistd_2.html#D1">AMISTD_2:def 1</a></i>;<br/><b>then consider </b><font color="Maroon">c<sub>4</sub></font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E13:122_1_1_1_10"/><i><font color="Green">E100</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font>
 <b>and </b><br/><a NAME="E14:122_1_1_1_10"/><i><font color="Green">E101</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 1
 <b>by </b><i><a class="ref" href="card_3.html#D6">CARD_3:def 6</a></i>;<br/><a NAME="E15:122_1_1_1_10"/><i><font color="Green">E102</font></i>: 
2 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E8:122_1_1_1_10"><i><font color="Green">E98</font></i></a>, <a class="ref" href="enumset1.html#D1">ENUMSET1:def 1</a></i>;<br/><a NAME="E16:122_1_1_1_10"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 2
 <b>by </b><i><a class="txt" href="scmfsa10.html#E7:122_1_1_1_10"><i><font color="Green">E97</font></i></a></i>;<br/><a NAME="E17:122_1_1_1_10"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R2">in</a>  <a href="card_3.html#K5">pi</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,2
 <b>by </b><i><a class="txt" href="scmfsa10.html#E15:122_1_1_1_10"><i><font color="Green">E102</font></i></a>, <a class="ref" href="amistd_2.html#D1">AMISTD_2:def 1</a></i>;<br/><b>then consider </b><font color="Maroon">c<sub>5</sub></font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E19:122_1_1_1_10"/><i><font color="Green">E103</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font>
 <b>and </b><br/><a NAME="E20:122_1_1_1_10"/><i><font color="Green">E104</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 2
 <b>by </b><i><a class="ref" href="card_3.html#D6">CARD_3:def 6</a></i>;<br/><a NAME="E21:122_1_1_1_10"/><i><font color="Green">E105</font></i>: 
3 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E8:122_1_1_1_10"><i><font color="Green">E98</font></i></a>, <a class="ref" href="enumset1.html#D1">ENUMSET1:def 1</a></i>;<br/><a NAME="E22:122_1_1_1_10"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 3 <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 3
 <b>by </b><i><a class="txt" href="scmfsa10.html#E7:122_1_1_1_10"><i><font color="Green">E97</font></i></a></i>;<br/><a NAME="E23:122_1_1_1_10"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 3 <a href="hidden.html#R2">in</a>  <a href="card_3.html#K5">pi</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,3
 <b>by </b><i><a class="txt" href="scmfsa10.html#E21:122_1_1_1_10"><i><font color="Green">E105</font></i></a>, <a class="ref" href="amistd_2.html#D1">AMISTD_2:def 1</a></i>;<br/><b>then consider </b><font color="Maroon">c<sub>6</sub></font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E25:122_1_1_1_10"/><i><font color="Green">E106</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font>
 <b>and </b><br/><a NAME="E26:122_1_1_1_10"/><i><font color="Green">E107</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="funct_1.html#K1">.</a> 3 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 3
 <b>by </b><i><a class="ref" href="card_3.html#D6">CARD_3:def 6</a></i>;<br/><b>consider </b><font color="Maroon">c<sub>7</sub></font> being   <a href="ami_1.html#NM3">Instruction</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> <b> such that </b><br/><a NAME="E28:122_1_1_1_10"/><i><font color="Green">E108</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">c<sub>7</sub></font>
 <b>and </b><br/><a NAME="E29:122_1_1_1_10"/><i><font color="Green">E109</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E13:122_1_1_1_10"><i><font color="Green">E100</font></i></a></i>;<br/><b>consider </b><font color="Maroon">c<sub>8</sub></font>, <font color="Maroon">c<sub>9</sub></font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">c<sub>10</sub></font> being    <a href="scmfsa_2.html#M2">FinSeq-Location</a> <b> such that </b><br/><a NAME="E31:122_1_1_1_10"/><i><font color="Green">E110</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font> <a href="scmfsa_2.html#K16">:=</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E1:122_1_1_1_10"><i><font color="Green">E94</font></i></a>, <a class="txt" href="scmfsa10.html#E29:122_1_1_1_10"><i><font color="Green">E109</font></i></a>, <a class="ref" href="scmfsa_2.html#T62">SCMFSA_2:62</a></i>;<br/><a NAME="E32:122_1_1_1_10"/><i><font color="Green">E111</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>8</sub></font></span><a href="finseq_4.html#K3">*&gt;</a></span>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E28:122_1_1_1_10"><i><font color="Green">E108</font></i></a>, <a class="txt" href="scmfsa10.html#E31:122_1_1_1_10"><i><font color="Green">E110</font></i></a>, <a class="ref" href="scmfsa10.html#T26" target="_self">Th26</a></i>;<br/><b>consider </b><font color="Maroon">c<sub>11</sub></font> being   <a href="ami_1.html#NM3">Instruction</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> <b> such that </b><br/><a NAME="E34:122_1_1_1_10"/><i><font color="Green">E112</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">c<sub>11</sub></font>
 <b>and </b><br/><a NAME="E35:122_1_1_1_10"/><i><font color="Green">E113</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E19:122_1_1_1_10"><i><font color="Green">E103</font></i></a></i>;<br/><b>consider </b><font color="Maroon">c<sub>12</sub></font>, <font color="Maroon">c<sub>13</sub></font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">c<sub>14</sub></font> being    <a href="scmfsa_2.html#M2">FinSeq-Location</a> <b> such that </b><br/><a NAME="E37:122_1_1_1_10"/><i><font color="Green">E114</font></i>: 
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>13</sub></font> <a href="scmfsa_2.html#K16">:=</a> <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>12</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E1:122_1_1_1_10"><i><font color="Green">E94</font></i></a>, <a class="txt" href="scmfsa10.html#E35:122_1_1_1_10"><i><font color="Green">E113</font></i></a>, <a class="ref" href="scmfsa_2.html#T62">SCMFSA_2:62</a></i>;<br/><a NAME="E38:122_1_1_1_10"/><i><font color="Green">E115</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>12</sub></font></span><a href="finseq_4.html#K3">*&gt;</a></span>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E34:122_1_1_1_10"><i><font color="Green">E112</font></i></a>, <a class="txt" href="scmfsa10.html#E37:122_1_1_1_10"><i><font color="Green">E114</font></i></a>, <a class="ref" href="scmfsa10.html#T26" target="_self">Th26</a></i>;<br/><b>consider </b><font color="Maroon">c<sub>15</sub></font> being   <a href="ami_1.html#NM3">Instruction</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> <b> such that </b><br/><a NAME="E40:122_1_1_1_10"/><i><font color="Green">E116</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a>  <a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">c<sub>15</sub></font>
 <b>and </b><br/><a NAME="E41:122_1_1_1_10"/><i><font color="Green">E117</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E25:122_1_1_1_10"><i><font color="Green">E106</font></i></a></i>;<br/><b>consider </b><font color="Maroon">c<sub>16</sub></font>, <font color="Maroon">c<sub>17</sub></font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">c<sub>18</sub></font> being    <a href="scmfsa_2.html#M2">FinSeq-Location</a> <b> such that </b><br/><a NAME="E43:122_1_1_1_10"/><i><font color="Green">E118</font></i>: 
<font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>17</sub></font> <a href="scmfsa_2.html#K16">:=</a> <font color="Maroon">c<sub>18</sub></font>,<font color="Maroon">c<sub>16</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E1:122_1_1_1_10"><i><font color="Green">E94</font></i></a>, <a class="txt" href="scmfsa10.html#E41:122_1_1_1_10"><i><font color="Green">E117</font></i></a>, <a class="ref" href="scmfsa_2.html#T62">SCMFSA_2:62</a></i>;<br/><a NAME="E44:122_1_1_1_10"/><i><font color="Green">E119</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>18</sub></font>,<font color="Maroon">c<sub>16</sub></font></span><a href="finseq_4.html#K3">*&gt;</a></span>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E40:122_1_1_1_10"><i><font color="Green">E116</font></i></a>, <a class="txt" href="scmfsa10.html#E43:122_1_1_1_10"><i><font color="Green">E118</font></i></a>, <a class="ref" href="scmfsa10.html#T26" target="_self">Th26</a></i>;<br/><a NAME="E45:122_1_1_1_10"/><i><font color="Green">E120</font></i>: 
 <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>16</sub></font></span><a href="finseq_4.html#K3">*&gt;</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="enumset1.html#K1">{</a><span class="default">1,2,3</span><a href="enumset1.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="finseq_3.html#T1">FINSEQ_3:1</a>, <a class="ref" href="finseq_3.html#T30">FINSEQ_3:30</a></i>;<br/><a NAME="E46:122_1_1_1_10"/>
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="enumset1.html#K1">{</a><span class="default">1,2,3</span><a href="enumset1.html#K1">}</a></span> holds <br/><span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>16</sub></font></span><a href="finseq_4.html#K3">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="122_1_1_1_10_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>19</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:122_1_1_1_10_1"/><i><font color="Green">E121</font></i>: 
<font color="Maroon">c<sub>19</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="enumset1.html#K1">{</a><span class="default">1,2,3</span><a href="enumset1.html#K1">}</a></span>
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_1_1_1_10_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:122_1_1_1_10_1_1"/>
( <font color="Maroon">c<sub>19</sub></font> <a href="hidden.html#R1">=</a> 1 or <font color="Maroon">c<sub>19</sub></font> <a href="hidden.html#R1">=</a> 2 or <font color="Maroon">c<sub>19</sub></font> <a href="hidden.html#R1">=</a> 3 )
 </span><b>by </b><i><a class="txt" href="scmfsa10.html#E1:122_1_1_1_10_1"><i><font color="Green">E121</font></i></a>, <a class="ref" href="enumset1.html#D1">ENUMSET1:def 1</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_1_1_1_10_1_1_1"><b>suppose </b></a><a NAME="E1:122_1_1_1_10_1_1_1"/><i><font color="Green">E122</font></i>: 
<font color="Maroon">c<sub>19</sub></font> <a href="hidden.html#R1">=</a> 1
 ;<br/><div class="add"><span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>16</sub></font></span><a href="finseq_4.html#K3">*&gt;</a></span> <a href="funct_1.html#K1">.</a> 1 = 
<font color="Maroon">c<sub>9</sub></font>
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 1
<b>by </b><i><a class="txt" href="scmfsa10.html#E14:122_1_1_1_10"><i><font color="Green">E101</font></i></a>, <a class="txt" href="scmfsa10.html#E32:122_1_1_1_10"><i><font color="Green">E111</font></i></a>, <a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
;<br/><b>hence </b><a NAME="E3:122_1_1_1_10_1_1_1"/>
<span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>16</sub></font></span><a href="finseq_4.html#K3">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>19</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>19</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E1:122_1_1_1_10_1_1_1"><i><font color="Green">E122</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_1_1_1_10_1_1_2"><b>suppose </b></a><a NAME="E1:122_1_1_1_10_1_1_2"/><i><font color="Green">E122</font></i>: 
<font color="Maroon">c<sub>19</sub></font> <a href="hidden.html#R1">=</a> 2
 ;<br/><div class="add"><span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>16</sub></font></span><a href="finseq_4.html#K3">*&gt;</a></span> <a href="funct_1.html#K1">.</a> 2 = 
<font color="Maroon">c<sub>14</sub></font>
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 2
<b>by </b><i><a class="txt" href="scmfsa10.html#E20:122_1_1_1_10"><i><font color="Green">E104</font></i></a>, <a class="txt" href="scmfsa10.html#E38:122_1_1_1_10"><i><font color="Green">E115</font></i></a>, <a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
;<br/><b>hence </b><a NAME="E3:122_1_1_1_10_1_1_2"/>
<span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>16</sub></font></span><a href="finseq_4.html#K3">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>19</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>19</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E1:122_1_1_1_10_1_1_2"><i><font color="Green">E122</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_1_1_1_10_1_1_3"><b>suppose </b></a><a NAME="E1:122_1_1_1_10_1_1_3"/><i><font color="Green">E122</font></i>: 
<font color="Maroon">c<sub>19</sub></font> <a href="hidden.html#R1">=</a> 3
 ;<br/><div class="add"><span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>16</sub></font></span><a href="finseq_4.html#K3">*&gt;</a></span> <a href="funct_1.html#K1">.</a> 3 = 
<font color="Maroon">c<sub>16</sub></font>
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 3
<b>by </b><i><a class="txt" href="scmfsa10.html#E26:122_1_1_1_10"><i><font color="Green">E107</font></i></a>, <a class="txt" href="scmfsa10.html#E44:122_1_1_1_10"><i><font color="Green">E119</font></i></a>, <a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
;<br/><b>hence </b><a NAME="E3:122_1_1_1_10_1_1_3"/>
<span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>16</sub></font></span><a href="finseq_4.html#K3">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>19</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>19</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E1:122_1_1_1_10_1_1_3"><i><font color="Green">E122</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div><a NAME="E47:122_1_1_1_10"/><b>then </b><i><font color="Green">E121</font></i>: 
<span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>16</sub></font></span><a href="finseq_4.html#K3">*&gt;</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E6:122_1_1_1_10"><i><font color="Green">E96</font></i></a>, <a class="txt" href="scmfsa10.html#E8:122_1_1_1_10"><i><font color="Green">E98</font></i></a>, <a class="txt" href="scmfsa10.html#E45:122_1_1_1_10"><i><font color="Green">E120</font></i></a>, <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/><a NAME="E48:122_1_1_1_10"/>
(  <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="scmfsa_2.html#K16">:=</a> <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>16</sub></font></span>)</span> <a href="hidden.html#R1">=</a> 9 &amp;  <a href="amistd_2.html#K4">AddressPart</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="scmfsa_2.html#K16">:=</a> <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>16</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>16</sub></font></span><a href="finseq_4.html#K3">*&gt;</a></span> )
 <b>by </b><i><a class="ref" href="scmfsa10.html#T26" target="_self">Th26</a>, <a class="ref" href="scmfsa_2.html#T50">SCMFSA_2:50</a></i>;<br/><b>hence </b><a NAME="E49:122_1_1_1_10"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E1:122_1_1_1_10"><i><font color="Green">E94</font></i></a>, <a class="txt" href="scmfsa10.html#E5:122_1_1_1_10"><i><font color="Green">E95</font></i></a>, <a class="txt" href="scmfsa10.html#E47:122_1_1_1_10"><i><font color="Green">E121</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_1_1_1_11"><b>suppose </b></a><a NAME="E1:122_1_1_1_11"/><i><font color="Green">E94</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 10
 ;<br/><div class="add"><b>take </b>
 <a href="amistd_2.html#K1">PA</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
; <i><font color="Red">:: according to </font></i><a class="ref" href="amistd_2.html#D2">AMISTD_2:def 2</a><br/><b>thus </b><a NAME="E2:122_1_1_1_11"/>
 <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a>  <a href="card_3.html#K4">product</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="amistd_2.html#T9">AMISTD_2:9</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/><b>assume </b><a NAME="E3:122_1_1_1_11"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="card_3.html#K4">product</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 ;<br/><b>then consider </b><font color="Maroon">c<sub>3</sub></font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E5:122_1_1_1_11"/><i><font color="Green">E95</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>and </b><br/><a NAME="E6:122_1_1_1_11"/><i><font color="Green">E96</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E7:122_1_1_1_11"/><i><font color="Green">E97</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> holds <br/><font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="card_3.html#D5">CARD_3:def 5</a></i>;<br/><a NAME="E8:122_1_1_1_11"/><i><font color="Green">E98</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="enumset1.html#K1">{</a><span class="default">1,2,3</span><a href="enumset1.html#K1">}</a></span>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E1:122_1_1_1_11"><i><font color="Green">E94</font></i></a>, <a class="ref" href="scmfsa10.html#T40" target="_self">Th40</a></i>;<br/><a NAME="E9:122_1_1_1_11"/><b>then </b><i><font color="Green">E99</font></i>: 
1 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="enumset1.html#D1">ENUMSET1:def 1</a></i>;<br/><a NAME="E10:122_1_1_1_11"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 1
 <b>by </b><i><a class="txt" href="scmfsa10.html#E7:122_1_1_1_11"><i><font color="Green">E97</font></i></a></i>;<br/><a NAME="E11:122_1_1_1_11"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R2">in</a>  <a href="card_3.html#K5">pi</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,1
 <b>by </b><i><a class="txt" href="scmfsa10.html#E9:122_1_1_1_11"><i><font color="Green">E99</font></i></a>, <a class="ref" href="amistd_2.html#D1">AMISTD_2:def 1</a></i>;<br/><b>then consider </b><font color="Maroon">c<sub>4</sub></font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E13:122_1_1_1_11"/><i><font color="Green">E100</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font>
 <b>and </b><br/><a NAME="E14:122_1_1_1_11"/><i><font color="Green">E101</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 1
 <b>by </b><i><a class="ref" href="card_3.html#D6">CARD_3:def 6</a></i>;<br/><a NAME="E15:122_1_1_1_11"/><i><font color="Green">E102</font></i>: 
2 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E8:122_1_1_1_11"><i><font color="Green">E98</font></i></a>, <a class="ref" href="enumset1.html#D1">ENUMSET1:def 1</a></i>;<br/><a NAME="E16:122_1_1_1_11"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 2
 <b>by </b><i><a class="txt" href="scmfsa10.html#E7:122_1_1_1_11"><i><font color="Green">E97</font></i></a></i>;<br/><a NAME="E17:122_1_1_1_11"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R2">in</a>  <a href="card_3.html#K5">pi</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,2
 <b>by </b><i><a class="txt" href="scmfsa10.html#E15:122_1_1_1_11"><i><font color="Green">E102</font></i></a>, <a class="ref" href="amistd_2.html#D1">AMISTD_2:def 1</a></i>;<br/><b>then consider </b><font color="Maroon">c<sub>5</sub></font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E19:122_1_1_1_11"/><i><font color="Green">E103</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font>
 <b>and </b><br/><a NAME="E20:122_1_1_1_11"/><i><font color="Green">E104</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 2
 <b>by </b><i><a class="ref" href="card_3.html#D6">CARD_3:def 6</a></i>;<br/><a NAME="E21:122_1_1_1_11"/><i><font color="Green">E105</font></i>: 
3 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E8:122_1_1_1_11"><i><font color="Green">E98</font></i></a>, <a class="ref" href="enumset1.html#D1">ENUMSET1:def 1</a></i>;<br/><a NAME="E22:122_1_1_1_11"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 3 <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 3
 <b>by </b><i><a class="txt" href="scmfsa10.html#E7:122_1_1_1_11"><i><font color="Green">E97</font></i></a></i>;<br/><a NAME="E23:122_1_1_1_11"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 3 <a href="hidden.html#R2">in</a>  <a href="card_3.html#K5">pi</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,3
 <b>by </b><i><a class="txt" href="scmfsa10.html#E21:122_1_1_1_11"><i><font color="Green">E105</font></i></a>, <a class="ref" href="amistd_2.html#D1">AMISTD_2:def 1</a></i>;<br/><b>then consider </b><font color="Maroon">c<sub>6</sub></font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E25:122_1_1_1_11"/><i><font color="Green">E106</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font>
 <b>and </b><br/><a NAME="E26:122_1_1_1_11"/><i><font color="Green">E107</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="funct_1.html#K1">.</a> 3 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 3
 <b>by </b><i><a class="ref" href="card_3.html#D6">CARD_3:def 6</a></i>;<br/><b>consider </b><font color="Maroon">c<sub>7</sub></font> being   <a href="ami_1.html#NM3">Instruction</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> <b> such that </b><br/><a NAME="E28:122_1_1_1_11"/><i><font color="Green">E108</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">c<sub>7</sub></font>
 <b>and </b><br/><a NAME="E29:122_1_1_1_11"/><i><font color="Green">E109</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E13:122_1_1_1_11"><i><font color="Green">E100</font></i></a></i>;<br/><b>consider </b><font color="Maroon">c<sub>8</sub></font>, <font color="Maroon">c<sub>9</sub></font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">c<sub>10</sub></font> being    <a href="scmfsa_2.html#M2">FinSeq-Location</a> <b> such that </b><br/><a NAME="E31:122_1_1_1_11"/><i><font color="Green">E110</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="scmfsa_2.html#K17">:=</a> <font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E1:122_1_1_1_11"><i><font color="Green">E94</font></i></a>, <a class="txt" href="scmfsa10.html#E29:122_1_1_1_11"><i><font color="Green">E109</font></i></a>, <a class="ref" href="scmfsa_2.html#T63">SCMFSA_2:63</a></i>;<br/><a NAME="E32:122_1_1_1_11"/><i><font color="Green">E111</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>8</sub></font></span><a href="finseq_4.html#K3">*&gt;</a></span>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E28:122_1_1_1_11"><i><font color="Green">E108</font></i></a>, <a class="txt" href="scmfsa10.html#E31:122_1_1_1_11"><i><font color="Green">E110</font></i></a>, <a class="ref" href="scmfsa10.html#T27" target="_self">Th27</a></i>;<br/><b>consider </b><font color="Maroon">c<sub>11</sub></font> being   <a href="ami_1.html#NM3">Instruction</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> <b> such that </b><br/><a NAME="E34:122_1_1_1_11"/><i><font color="Green">E112</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">c<sub>11</sub></font>
 <b>and </b><br/><a NAME="E35:122_1_1_1_11"/><i><font color="Green">E113</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E19:122_1_1_1_11"><i><font color="Green">E103</font></i></a></i>;<br/><b>consider </b><font color="Maroon">c<sub>12</sub></font>, <font color="Maroon">c<sub>13</sub></font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">c<sub>14</sub></font> being    <a href="scmfsa_2.html#M2">FinSeq-Location</a> <b> such that </b><br/><a NAME="E37:122_1_1_1_11"/><i><font color="Green">E114</font></i>: 
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>12</sub></font> <a href="scmfsa_2.html#K17">:=</a> <font color="Maroon">c<sub>13</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E1:122_1_1_1_11"><i><font color="Green">E94</font></i></a>, <a class="txt" href="scmfsa10.html#E35:122_1_1_1_11"><i><font color="Green">E113</font></i></a>, <a class="ref" href="scmfsa_2.html#T63">SCMFSA_2:63</a></i>;<br/><a NAME="E38:122_1_1_1_11"/><i><font color="Green">E115</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>12</sub></font></span><a href="finseq_4.html#K3">*&gt;</a></span>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E34:122_1_1_1_11"><i><font color="Green">E112</font></i></a>, <a class="txt" href="scmfsa10.html#E37:122_1_1_1_11"><i><font color="Green">E114</font></i></a>, <a class="ref" href="scmfsa10.html#T27" target="_self">Th27</a></i>;<br/><b>consider </b><font color="Maroon">c<sub>15</sub></font> being   <a href="ami_1.html#NM3">Instruction</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> <b> such that </b><br/><a NAME="E40:122_1_1_1_11"/><i><font color="Green">E116</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a>  <a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">c<sub>15</sub></font>
 <b>and </b><br/><a NAME="E41:122_1_1_1_11"/><i><font color="Green">E117</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E25:122_1_1_1_11"><i><font color="Green">E106</font></i></a></i>;<br/><b>consider </b><font color="Maroon">c<sub>16</sub></font>, <font color="Maroon">c<sub>17</sub></font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">c<sub>18</sub></font> being    <a href="scmfsa_2.html#M2">FinSeq-Location</a> <b> such that </b><br/><a NAME="E43:122_1_1_1_11"/><i><font color="Green">E118</font></i>: 
<font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>18</sub></font>,<font color="Maroon">c<sub>16</sub></font> <a href="scmfsa_2.html#K17">:=</a> <font color="Maroon">c<sub>17</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E1:122_1_1_1_11"><i><font color="Green">E94</font></i></a>, <a class="txt" href="scmfsa10.html#E41:122_1_1_1_11"><i><font color="Green">E117</font></i></a>, <a class="ref" href="scmfsa_2.html#T63">SCMFSA_2:63</a></i>;<br/><a NAME="E44:122_1_1_1_11"/><i><font color="Green">E119</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>18</sub></font>,<font color="Maroon">c<sub>16</sub></font></span><a href="finseq_4.html#K3">*&gt;</a></span>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E40:122_1_1_1_11"><i><font color="Green">E116</font></i></a>, <a class="txt" href="scmfsa10.html#E43:122_1_1_1_11"><i><font color="Green">E118</font></i></a>, <a class="ref" href="scmfsa10.html#T27" target="_self">Th27</a></i>;<br/><a NAME="E45:122_1_1_1_11"/><i><font color="Green">E120</font></i>: 
 <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>16</sub></font></span><a href="finseq_4.html#K3">*&gt;</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="enumset1.html#K1">{</a><span class="default">1,2,3</span><a href="enumset1.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="finseq_3.html#T1">FINSEQ_3:1</a>, <a class="ref" href="finseq_3.html#T30">FINSEQ_3:30</a></i>;<br/><a NAME="E46:122_1_1_1_11"/>
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="enumset1.html#K1">{</a><span class="default">1,2,3</span><a href="enumset1.html#K1">}</a></span> holds <br/><span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>16</sub></font></span><a href="finseq_4.html#K3">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="122_1_1_1_11_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>19</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:122_1_1_1_11_1"/><i><font color="Green">E121</font></i>: 
<font color="Maroon">c<sub>19</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="enumset1.html#K1">{</a><span class="default">1,2,3</span><a href="enumset1.html#K1">}</a></span>
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_1_1_1_11_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:122_1_1_1_11_1_1"/>
( <font color="Maroon">c<sub>19</sub></font> <a href="hidden.html#R1">=</a> 1 or <font color="Maroon">c<sub>19</sub></font> <a href="hidden.html#R1">=</a> 2 or <font color="Maroon">c<sub>19</sub></font> <a href="hidden.html#R1">=</a> 3 )
 </span><b>by </b><i><a class="txt" href="scmfsa10.html#E1:122_1_1_1_11_1"><i><font color="Green">E121</font></i></a>, <a class="ref" href="enumset1.html#D1">ENUMSET1:def 1</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_1_1_1_11_1_1_1"><b>suppose </b></a><a NAME="E1:122_1_1_1_11_1_1_1"/><i><font color="Green">E122</font></i>: 
<font color="Maroon">c<sub>19</sub></font> <a href="hidden.html#R1">=</a> 1
 ;<br/><div class="add"><span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>16</sub></font></span><a href="finseq_4.html#K3">*&gt;</a></span> <a href="funct_1.html#K1">.</a> 1 = 
<font color="Maroon">c<sub>9</sub></font>
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 1
<b>by </b><i><a class="txt" href="scmfsa10.html#E14:122_1_1_1_11"><i><font color="Green">E101</font></i></a>, <a class="txt" href="scmfsa10.html#E32:122_1_1_1_11"><i><font color="Green">E111</font></i></a>, <a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
;<br/><b>hence </b><a NAME="E3:122_1_1_1_11_1_1_1"/>
<span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>16</sub></font></span><a href="finseq_4.html#K3">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>19</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>19</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E1:122_1_1_1_11_1_1_1"><i><font color="Green">E122</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_1_1_1_11_1_1_2"><b>suppose </b></a><a NAME="E1:122_1_1_1_11_1_1_2"/><i><font color="Green">E122</font></i>: 
<font color="Maroon">c<sub>19</sub></font> <a href="hidden.html#R1">=</a> 2
 ;<br/><div class="add"><span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>16</sub></font></span><a href="finseq_4.html#K3">*&gt;</a></span> <a href="funct_1.html#K1">.</a> 2 = 
<font color="Maroon">c<sub>14</sub></font>
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 2
<b>by </b><i><a class="txt" href="scmfsa10.html#E20:122_1_1_1_11"><i><font color="Green">E104</font></i></a>, <a class="txt" href="scmfsa10.html#E38:122_1_1_1_11"><i><font color="Green">E115</font></i></a>, <a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
;<br/><b>hence </b><a NAME="E3:122_1_1_1_11_1_1_2"/>
<span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>16</sub></font></span><a href="finseq_4.html#K3">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>19</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>19</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E1:122_1_1_1_11_1_1_2"><i><font color="Green">E122</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_1_1_1_11_1_1_3"><b>suppose </b></a><a NAME="E1:122_1_1_1_11_1_1_3"/><i><font color="Green">E122</font></i>: 
<font color="Maroon">c<sub>19</sub></font> <a href="hidden.html#R1">=</a> 3
 ;<br/><div class="add"><span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>16</sub></font></span><a href="finseq_4.html#K3">*&gt;</a></span> <a href="funct_1.html#K1">.</a> 3 = 
<font color="Maroon">c<sub>16</sub></font>
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 3
<b>by </b><i><a class="txt" href="scmfsa10.html#E26:122_1_1_1_11"><i><font color="Green">E107</font></i></a>, <a class="txt" href="scmfsa10.html#E44:122_1_1_1_11"><i><font color="Green">E119</font></i></a>, <a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
;<br/><b>hence </b><a NAME="E3:122_1_1_1_11_1_1_3"/>
<span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>16</sub></font></span><a href="finseq_4.html#K3">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>19</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>19</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E1:122_1_1_1_11_1_1_3"><i><font color="Green">E122</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div><a NAME="E47:122_1_1_1_11"/><b>then </b><i><font color="Green">E121</font></i>: 
<span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>16</sub></font></span><a href="finseq_4.html#K3">*&gt;</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E6:122_1_1_1_11"><i><font color="Green">E96</font></i></a>, <a class="txt" href="scmfsa10.html#E8:122_1_1_1_11"><i><font color="Green">E98</font></i></a>, <a class="txt" href="scmfsa10.html#E45:122_1_1_1_11"><i><font color="Green">E120</font></i></a>, <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/><a NAME="E48:122_1_1_1_11"/>
(  <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>16</sub></font> <a href="scmfsa_2.html#K17">:=</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="hidden.html#R1">=</a> 10 &amp;  <a href="amistd_2.html#K4">AddressPart</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>16</sub></font> <a href="scmfsa_2.html#K17">:=</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>16</sub></font></span><a href="finseq_4.html#K3">*&gt;</a></span> )
 <b>by </b><i><a class="ref" href="scmfsa10.html#T27" target="_self">Th27</a>, <a class="ref" href="scmfsa_2.html#T51">SCMFSA_2:51</a></i>;<br/><b>hence </b><a NAME="E49:122_1_1_1_11"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E1:122_1_1_1_11"><i><font color="Green">E94</font></i></a>, <a class="txt" href="scmfsa10.html#E5:122_1_1_1_11"><i><font color="Green">E95</font></i></a>, <a class="txt" href="scmfsa10.html#E47:122_1_1_1_11"><i><font color="Green">E121</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_1_1_1_12"><b>suppose </b></a><a NAME="E1:122_1_1_1_12"/><i><font color="Green">E94</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 11
 ;<br/><div class="add"><b>take </b>
 <a href="amistd_2.html#K1">PA</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
; <i><font color="Red">:: according to </font></i><a class="ref" href="amistd_2.html#D2">AMISTD_2:def 2</a><br/><b>thus </b><a NAME="E2:122_1_1_1_12"/>
 <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a>  <a href="card_3.html#K4">product</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="amistd_2.html#T9">AMISTD_2:9</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/><b>assume </b><a NAME="E3:122_1_1_1_12"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="card_3.html#K4">product</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 ;<br/><b>then consider </b><font color="Maroon">c<sub>3</sub></font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E5:122_1_1_1_12"/><i><font color="Green">E95</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>and </b><br/><a NAME="E6:122_1_1_1_12"/><i><font color="Green">E96</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E7:122_1_1_1_12"/><i><font color="Green">E97</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> holds <br/><font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="card_3.html#D5">CARD_3:def 5</a></i>;<br/><a NAME="E8:122_1_1_1_12"/><i><font color="Green">E98</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E1:122_1_1_1_12"><i><font color="Green">E94</font></i></a>, <a class="ref" href="scmfsa10.html#T41" target="_self">Th41</a></i>;<br/><a NAME="E9:122_1_1_1_12"/><b>then </b><i><font color="Green">E99</font></i>: 
1 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><a NAME="E10:122_1_1_1_12"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 1
 <b>by </b><i><a class="txt" href="scmfsa10.html#E7:122_1_1_1_12"><i><font color="Green">E97</font></i></a></i>;<br/><a NAME="E11:122_1_1_1_12"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R2">in</a>  <a href="card_3.html#K5">pi</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,1
 <b>by </b><i><a class="txt" href="scmfsa10.html#E9:122_1_1_1_12"><i><font color="Green">E99</font></i></a>, <a class="ref" href="amistd_2.html#D1">AMISTD_2:def 1</a></i>;<br/><b>then consider </b><font color="Maroon">c<sub>4</sub></font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E13:122_1_1_1_12"/><i><font color="Green">E100</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font>
 <b>and </b><br/><a NAME="E14:122_1_1_1_12"/><i><font color="Green">E101</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 1
 <b>by </b><i><a class="ref" href="card_3.html#D6">CARD_3:def 6</a></i>;<br/><a NAME="E15:122_1_1_1_12"/><i><font color="Green">E102</font></i>: 
2 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E8:122_1_1_1_12"><i><font color="Green">E98</font></i></a>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><a NAME="E16:122_1_1_1_12"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 2
 <b>by </b><i><a class="txt" href="scmfsa10.html#E7:122_1_1_1_12"><i><font color="Green">E97</font></i></a></i>;<br/><a NAME="E17:122_1_1_1_12"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R2">in</a>  <a href="card_3.html#K5">pi</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,2
 <b>by </b><i><a class="txt" href="scmfsa10.html#E15:122_1_1_1_12"><i><font color="Green">E102</font></i></a>, <a class="ref" href="amistd_2.html#D1">AMISTD_2:def 1</a></i>;<br/><b>then consider </b><font color="Maroon">c<sub>5</sub></font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E19:122_1_1_1_12"/><i><font color="Green">E103</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font>
 <b>and </b><br/><a NAME="E20:122_1_1_1_12"/><i><font color="Green">E104</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 2
 <b>by </b><i><a class="ref" href="card_3.html#D6">CARD_3:def 6</a></i>;<br/><b>consider </b><font color="Maroon">c<sub>6</sub></font> being   <a href="ami_1.html#NM3">Instruction</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> <b> such that </b><br/><a NAME="E22:122_1_1_1_12"/><i><font color="Green">E105</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">c<sub>6</sub></font>
 <b>and </b><br/><a NAME="E23:122_1_1_1_12"/><i><font color="Green">E106</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E13:122_1_1_1_12"><i><font color="Green">E100</font></i></a></i>;<br/><b>consider </b><font color="Maroon">c<sub>7</sub></font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">c<sub>8</sub></font> being    <a href="scmfsa_2.html#M2">FinSeq-Location</a> <b> such that </b><br/><a NAME="E25:122_1_1_1_12"/><i><font color="Green">E107</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> <a href="scmfsa_2.html#K18">:=len</a> <font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E1:122_1_1_1_12"><i><font color="Green">E94</font></i></a>, <a class="txt" href="scmfsa10.html#E23:122_1_1_1_12"><i><font color="Green">E106</font></i></a>, <a class="ref" href="scmfsa_2.html#T64">SCMFSA_2:64</a></i>;<br/><a NAME="E26:122_1_1_1_12"/><i><font color="Green">E108</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E22:122_1_1_1_12"><i><font color="Green">E105</font></i></a>, <a class="txt" href="scmfsa10.html#E25:122_1_1_1_12"><i><font color="Green">E107</font></i></a>, <a class="ref" href="scmfsa10.html#T28" target="_self">Th28</a></i>;<br/><b>consider </b><font color="Maroon">c<sub>9</sub></font> being   <a href="ami_1.html#NM3">Instruction</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> <b> such that </b><br/><a NAME="E28:122_1_1_1_12"/><i><font color="Green">E109</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">c<sub>9</sub></font>
 <b>and </b><br/><a NAME="E29:122_1_1_1_12"/><i><font color="Green">E110</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E19:122_1_1_1_12"><i><font color="Green">E103</font></i></a></i>;<br/><b>consider </b><font color="Maroon">c<sub>10</sub></font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">c<sub>11</sub></font> being    <a href="scmfsa_2.html#M2">FinSeq-Location</a> <b> such that </b><br/><a NAME="E31:122_1_1_1_12"/><i><font color="Green">E111</font></i>: 
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>10</sub></font> <a href="scmfsa_2.html#K18">:=len</a> <font color="Maroon">c<sub>11</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E1:122_1_1_1_12"><i><font color="Green">E94</font></i></a>, <a class="txt" href="scmfsa10.html#E29:122_1_1_1_12"><i><font color="Green">E110</font></i></a>, <a class="ref" href="scmfsa_2.html#T64">SCMFSA_2:64</a></i>;<br/><a NAME="E32:122_1_1_1_12"/><i><font color="Green">E112</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E28:122_1_1_1_12"><i><font color="Green">E109</font></i></a>, <a class="txt" href="scmfsa10.html#E31:122_1_1_1_12"><i><font color="Green">E111</font></i></a>, <a class="ref" href="scmfsa10.html#T28" target="_self">Th28</a></i>;<br/><a NAME="E33:122_1_1_1_12"/><i><font color="Green">E113</font></i>: 
 <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i><a class="ref" href="finseq_1.html#T4">FINSEQ_1:4</a>, <a class="ref" href="finseq_3.html#T29">FINSEQ_3:29</a></i>;<br/><a NAME="E34:122_1_1_1_12"/>
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span> holds <br/><span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="122_1_1_1_12_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>12</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:122_1_1_1_12_1"/><i><font color="Green">E114</font></i>: 
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span>
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_1_1_1_12_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:122_1_1_1_12_1_1"/>
( <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> 1 or <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> 2 )
 </span><b>by </b><i><a class="txt" href="scmfsa10.html#E1:122_1_1_1_12_1"><i><font color="Green">E114</font></i></a>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_1_1_1_12_1_1_1"><b>suppose </b></a><a NAME="E1:122_1_1_1_12_1_1_1"/><i><font color="Green">E115</font></i>: 
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> 1
 ;<br/><div class="add"><span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="funct_1.html#K1">.</a> 1 = 
<font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 1
<b>by </b><i><a class="txt" href="scmfsa10.html#E14:122_1_1_1_12"><i><font color="Green">E101</font></i></a>, <a class="txt" href="scmfsa10.html#E26:122_1_1_1_12"><i><font color="Green">E108</font></i></a>, <a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
;<br/><b>hence </b><a NAME="E3:122_1_1_1_12_1_1_1"/>
<span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E1:122_1_1_1_12_1_1_1"><i><font color="Green">E115</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_1_1_1_12_1_1_2"><b>suppose </b></a><a NAME="E1:122_1_1_1_12_1_1_2"/><i><font color="Green">E115</font></i>: 
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> 2
 ;<br/><div class="add"><span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="funct_1.html#K1">.</a> 2 = 
<font color="Maroon">c<sub>11</sub></font>
<b>by </b><i><a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 2
<b>by </b><i><a class="txt" href="scmfsa10.html#E20:122_1_1_1_12"><i><font color="Green">E104</font></i></a>, <a class="txt" href="scmfsa10.html#E32:122_1_1_1_12"><i><font color="Green">E112</font></i></a>, <a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
;<br/><b>hence </b><a NAME="E3:122_1_1_1_12_1_1_2"/>
<span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E1:122_1_1_1_12_1_1_2"><i><font color="Green">E115</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div><a NAME="E35:122_1_1_1_12"/><b>then </b><i><font color="Green">E114</font></i>: 
<span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E6:122_1_1_1_12"><i><font color="Green">E96</font></i></a>, <a class="txt" href="scmfsa10.html#E8:122_1_1_1_12"><i><font color="Green">E98</font></i></a>, <a class="txt" href="scmfsa10.html#E33:122_1_1_1_12"><i><font color="Green">E113</font></i></a>, <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/><a NAME="E36:122_1_1_1_12"/>
(  <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="scmfsa_2.html#K18">:=len</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="hidden.html#R1">=</a> 11 &amp;  <a href="amistd_2.html#K4">AddressPart</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="scmfsa_2.html#K18">:=len</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span> )
 <b>by </b><i><a class="ref" href="scmfsa10.html#T28" target="_self">Th28</a>, <a class="ref" href="scmfsa_2.html#T52">SCMFSA_2:52</a></i>;<br/><b>hence </b><a NAME="E37:122_1_1_1_12"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E1:122_1_1_1_12"><i><font color="Green">E94</font></i></a>, <a class="txt" href="scmfsa10.html#E5:122_1_1_1_12"><i><font color="Green">E95</font></i></a>, <a class="txt" href="scmfsa10.html#E35:122_1_1_1_12"><i><font color="Green">E114</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_1_1_1_13"><b>suppose </b></a><a NAME="E1:122_1_1_1_13"/><i><font color="Green">E94</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 12
 ;<br/><div class="add"><b>take </b>
 <a href="amistd_2.html#K1">PA</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
; <i><font color="Red">:: according to </font></i><a class="ref" href="amistd_2.html#D2">AMISTD_2:def 2</a><br/><b>thus </b><a NAME="E2:122_1_1_1_13"/>
 <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a>  <a href="card_3.html#K4">product</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="amistd_2.html#T9">AMISTD_2:9</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/><b>assume </b><a NAME="E3:122_1_1_1_13"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="card_3.html#K4">product</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 ;<br/><b>then consider </b><font color="Maroon">c<sub>3</sub></font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E5:122_1_1_1_13"/><i><font color="Green">E95</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>and </b><br/><a NAME="E6:122_1_1_1_13"/><i><font color="Green">E96</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E7:122_1_1_1_13"/><i><font color="Green">E97</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> holds <br/><font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="card_3.html#D5">CARD_3:def 5</a></i>;<br/><a NAME="E8:122_1_1_1_13"/><i><font color="Green">E98</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E1:122_1_1_1_13"><i><font color="Green">E94</font></i></a>, <a class="ref" href="scmfsa10.html#T42" target="_self">Th42</a></i>;<br/><a NAME="E9:122_1_1_1_13"/><b>then </b><i><font color="Green">E99</font></i>: 
1 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><a NAME="E10:122_1_1_1_13"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 1
 <b>by </b><i><a class="txt" href="scmfsa10.html#E7:122_1_1_1_13"><i><font color="Green">E97</font></i></a></i>;<br/><a NAME="E11:122_1_1_1_13"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R2">in</a>  <a href="card_3.html#K5">pi</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,1
 <b>by </b><i><a class="txt" href="scmfsa10.html#E9:122_1_1_1_13"><i><font color="Green">E99</font></i></a>, <a class="ref" href="amistd_2.html#D1">AMISTD_2:def 1</a></i>;<br/><b>then consider </b><font color="Maroon">c<sub>4</sub></font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E13:122_1_1_1_13"/><i><font color="Green">E100</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font>
 <b>and </b><br/><a NAME="E14:122_1_1_1_13"/><i><font color="Green">E101</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 1
 <b>by </b><i><a class="ref" href="card_3.html#D6">CARD_3:def 6</a></i>;<br/><a NAME="E15:122_1_1_1_13"/><i><font color="Green">E102</font></i>: 
2 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E8:122_1_1_1_13"><i><font color="Green">E98</font></i></a>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><a NAME="E16:122_1_1_1_13"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 2
 <b>by </b><i><a class="txt" href="scmfsa10.html#E7:122_1_1_1_13"><i><font color="Green">E97</font></i></a></i>;<br/><a NAME="E17:122_1_1_1_13"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R2">in</a>  <a href="card_3.html#K5">pi</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,2
 <b>by </b><i><a class="txt" href="scmfsa10.html#E15:122_1_1_1_13"><i><font color="Green">E102</font></i></a>, <a class="ref" href="amistd_2.html#D1">AMISTD_2:def 1</a></i>;<br/><b>then consider </b><font color="Maroon">c<sub>5</sub></font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E19:122_1_1_1_13"/><i><font color="Green">E103</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font>
 <b>and </b><br/><a NAME="E20:122_1_1_1_13"/><i><font color="Green">E104</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 2
 <b>by </b><i><a class="ref" href="card_3.html#D6">CARD_3:def 6</a></i>;<br/><b>consider </b><font color="Maroon">c<sub>6</sub></font> being   <a href="ami_1.html#NM3">Instruction</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> <b> such that </b><br/><a NAME="E22:122_1_1_1_13"/><i><font color="Green">E105</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">c<sub>6</sub></font>
 <b>and </b><br/><a NAME="E23:122_1_1_1_13"/><i><font color="Green">E106</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E13:122_1_1_1_13"><i><font color="Green">E100</font></i></a></i>;<br/><b>consider </b><font color="Maroon">c<sub>7</sub></font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">c<sub>8</sub></font> being    <a href="scmfsa_2.html#M2">FinSeq-Location</a> <b> such that </b><br/><a NAME="E25:122_1_1_1_13"/><i><font color="Green">E107</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E1:122_1_1_1_13"><i><font color="Green">E94</font></i></a>, <a class="txt" href="scmfsa10.html#E23:122_1_1_1_13"><i><font color="Green">E106</font></i></a>, <a class="ref" href="scmfsa_2.html#T65">SCMFSA_2:65</a></i>;<br/><a NAME="E26:122_1_1_1_13"/><i><font color="Green">E108</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E22:122_1_1_1_13"><i><font color="Green">E105</font></i></a>, <a class="txt" href="scmfsa10.html#E25:122_1_1_1_13"><i><font color="Green">E107</font></i></a>, <a class="ref" href="scmfsa10.html#T29" target="_self">Th29</a></i>;<br/><b>consider </b><font color="Maroon">c<sub>9</sub></font> being   <a href="ami_1.html#NM3">Instruction</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> <b> such that </b><br/><a NAME="E28:122_1_1_1_13"/><i><font color="Green">E109</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">c<sub>9</sub></font>
 <b>and </b><br/><a NAME="E29:122_1_1_1_13"/><i><font color="Green">E110</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E19:122_1_1_1_13"><i><font color="Green">E103</font></i></a></i>;<br/><b>consider </b><font color="Maroon">c<sub>10</sub></font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">c<sub>11</sub></font> being    <a href="scmfsa_2.html#M2">FinSeq-Location</a> <b> such that </b><br/><a NAME="E31:122_1_1_1_13"/><i><font color="Green">E111</font></i>: 
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>11</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E1:122_1_1_1_13"><i><font color="Green">E94</font></i></a>, <a class="txt" href="scmfsa10.html#E29:122_1_1_1_13"><i><font color="Green">E110</font></i></a>, <a class="ref" href="scmfsa_2.html#T65">SCMFSA_2:65</a></i>;<br/><a NAME="E32:122_1_1_1_13"/><i><font color="Green">E112</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E28:122_1_1_1_13"><i><font color="Green">E109</font></i></a>, <a class="txt" href="scmfsa10.html#E31:122_1_1_1_13"><i><font color="Green">E111</font></i></a>, <a class="ref" href="scmfsa10.html#T29" target="_self">Th29</a></i>;<br/><a NAME="E33:122_1_1_1_13"/><i><font color="Green">E113</font></i>: 
 <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i><a class="ref" href="finseq_1.html#T4">FINSEQ_1:4</a>, <a class="ref" href="finseq_3.html#T29">FINSEQ_3:29</a></i>;<br/><a NAME="E34:122_1_1_1_13"/>
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span> holds <br/><span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="122_1_1_1_13_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>12</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:122_1_1_1_13_1"/><i><font color="Green">E114</font></i>: 
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span>
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_1_1_1_13_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:122_1_1_1_13_1_1"/>
( <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> 1 or <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> 2 )
 </span><b>by </b><i><a class="txt" href="scmfsa10.html#E1:122_1_1_1_13_1"><i><font color="Green">E114</font></i></a>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_1_1_1_13_1_1_1"><b>suppose </b></a><a NAME="E1:122_1_1_1_13_1_1_1"/><i><font color="Green">E115</font></i>: 
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> 1
 ;<br/><div class="add"><span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="funct_1.html#K1">.</a> 1 = 
<font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 1
<b>by </b><i><a class="txt" href="scmfsa10.html#E14:122_1_1_1_13"><i><font color="Green">E101</font></i></a>, <a class="txt" href="scmfsa10.html#E26:122_1_1_1_13"><i><font color="Green">E108</font></i></a>, <a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
;<br/><b>hence </b><a NAME="E3:122_1_1_1_13_1_1_1"/>
<span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E1:122_1_1_1_13_1_1_1"><i><font color="Green">E115</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_1_1_1_13_1_1_2"><b>suppose </b></a><a NAME="E1:122_1_1_1_13_1_1_2"/><i><font color="Green">E115</font></i>: 
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> 2
 ;<br/><div class="add"><span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="funct_1.html#K1">.</a> 2 = 
<font color="Maroon">c<sub>11</sub></font>
<b>by </b><i><a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 2
<b>by </b><i><a class="txt" href="scmfsa10.html#E20:122_1_1_1_13"><i><font color="Green">E104</font></i></a>, <a class="txt" href="scmfsa10.html#E32:122_1_1_1_13"><i><font color="Green">E112</font></i></a>, <a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
;<br/><b>hence </b><a NAME="E3:122_1_1_1_13_1_1_2"/>
<span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E1:122_1_1_1_13_1_1_2"><i><font color="Green">E115</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div><a NAME="E35:122_1_1_1_13"/><b>then </b><i><font color="Green">E114</font></i>: 
<span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E6:122_1_1_1_13"><i><font color="Green">E96</font></i></a>, <a class="txt" href="scmfsa10.html#E8:122_1_1_1_13"><i><font color="Green">E98</font></i></a>, <a class="txt" href="scmfsa10.html#E33:122_1_1_1_13"><i><font color="Green">E113</font></i></a>, <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/><a NAME="E36:122_1_1_1_13"/>
(  <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="hidden.html#R1">=</a> 12 &amp;  <a href="amistd_2.html#K4">AddressPart</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span> )
 <b>by </b><i><a class="ref" href="scmfsa10.html#T29" target="_self">Th29</a>, <a class="ref" href="scmfsa_2.html#T53">SCMFSA_2:53</a></i>;<br/><b>hence </b><a NAME="E37:122_1_1_1_13"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E1:122_1_1_1_13"><i><font color="Green">E94</font></i></a>, <a class="txt" href="scmfsa10.html#E5:122_1_1_1_13"><i><font color="Green">E95</font></i></a>, <a class="txt" href="scmfsa10.html#E35:122_1_1_1_13"><i><font color="Green">E114</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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