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<b>let </b><font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font> be   <a href="ami_1.html#NM4">State</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> ;<br/><b>let </b><font color="Maroon">c<sub>6</sub></font> be   <a href="subset_1.html#NM2">Subset</a> of <a href="scmfsa_2.html#K2">Int-Locations</a> ;<br/><b>let </b><font color="Maroon">c<sub>7</sub></font> be   <a href="subset_1.html#NM2">Subset</a> of <a href="scmfsa_2.html#K3">FinSeq-Locations</a> ;<br/>







<a NAME="E1:6"/><i><font color="Green">E6</font></i>: 
(  <a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>4</sub></font> &amp;  <a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>5</sub></font> )
 
<b>by </b><i><a class="ref" href="scmfsa_2.html#T69">SCMFSA_2:69</a></i>;<br/>
<a NAME="E2:6"/><i><font color="Green">E7</font></i>: 
(  <a href="scmfsa_2.html#K3">FinSeq-Locations</a>  <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>4</sub></font> &amp;  <a href="scmfsa_2.html#K3">FinSeq-Locations</a>  <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>5</sub></font> )
 
<b>by </b><i><a class="ref" href="scmfsa_2.html#T70">SCMFSA_2:70</a></i>;<br/>
<a NAME="E3:6"/><i><font color="Green">E8</font></i>: 
( <font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>5</sub></font> )
 
<b>by </b><i><a class="txt" href="sfmastr2.html#E1:6"><i><font color="Green">E6</font></i></a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E4:6"/><i><font color="Green">E9</font></i>: 
( <font color="Maroon">c<sub>7</sub></font> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>5</sub></font> )
 
<b>by </b><i><a class="txt" href="sfmastr2.html#E2:6"><i><font color="Green">E7</font></i></a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E5:6"/><b>then </b><i><font color="Green">E10</font></i>: 
( <font color="Maroon">c<sub>6</sub></font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">c<sub>7</sub></font> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">c<sub>7</sub></font> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>5</sub></font> )
 
<b>by </b><i><a class="txt" href="sfmastr2.html#E3:6"><i><font color="Green">E8</font></i></a>, <a class="ref" href="xboole_1.html#T8">XBOOLE_1:8</a></i>;<br/>
<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:6_1"/><i><font color="Green">E11</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>
 ;<br/><div><b>hereby </b>
<div class="add"><b>let </b><font color="Maroon">c<sub>8</sub></font> be    <a href="scmfsa_2.html#M1">Int-Location</a> ;<br/><b>assume </b><a NAME="E1:6_1_1"/>
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>6</sub></font>
 ;<br/><a NAME="E2:6_1_1"/><b>then </b>
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>6</sub></font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><b>hence </b><a NAME="E3:6_1_1"/>
<font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="txt" href="sfmastr2.html#E5:6"><i><font color="Green">E10</font></i></a>, <a class="txt" href="sfmastr2.html#E1:6_1"><i><font color="Green">E11</font></i></a>, <a class="ref" href="scmfsa6a.html#T9">SCMFSA6A:9</a></i>;<br/></div>
<b>end;</b></div><b>let </b><font color="Maroon">c<sub>8</sub></font> be    <a href="scmfsa_2.html#M2">FinSeq-Location</a> ;<br/><b>assume </b><a NAME="E3:6_1"/>
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>7</sub></font>
 ;<br/><a NAME="E4:6_1"/><b>then </b>
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>6</sub></font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><b>hence </b><a NAME="E5:6_1"/>
<font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="txt" href="sfmastr2.html#E5:6"><i><font color="Green">E10</font></i></a>, <a class="txt" href="sfmastr2.html#E1:6_1"><i><font color="Green">E11</font></i></a>, <a class="ref" href="scmfsa6a.html#T9">SCMFSA6A:9</a></i>;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E7:6"/><i><font color="Green">E11</font></i>: 
( ( for <font color="Olive">b<sub>1</sub></font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>6</sub></font> holds <br/><font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Olive">b<sub>1</sub></font> ) &amp; ( for <font color="Olive">b<sub>1</sub></font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>7</sub></font> holds <br/><font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K21">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K21">.</a> <font color="Olive">b<sub>1</sub></font> ) )
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="6_2"><b>now </b></a><div class="add"><div><b>hereby </b>
<div class="add"><b>let </b><font color="Maroon">c<sub>8</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:6_2_1"/><i><font color="Green">E12</font></i>: 
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>6</sub></font>
 ;<br/><b>then reconsider </b><font color="Maroon">c<sub>9</sub></font> = <font color="Maroon">c<sub>8</sub></font> as    <a href="scmfsa_2.html#M1">Int-Location</a>  <b>by </b><i><a class="ref" href="scmfsa_2.html#T11">SCMFSA_2:11</a></i>;<br/><b>thus </b><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>8</sub></font> = 
<font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>9</sub></font>
<b>by </b><i><a class="txt" href="sfmastr2.html#E7:6"><i><font color="Green">E11</font></i></a>, <a class="txt" href="sfmastr2.html#E1:6_2_1"><i><font color="Green">E12</font></i></a></i>
<br/>.= 
<font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>8</sub></font>

;<br/></div>
<b>end;</b></div><b>let </b><font color="Maroon">c<sub>8</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E2:6_2"/><i><font color="Green">E12</font></i>: 
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>7</sub></font>
 ;<br/><b>then reconsider </b><font color="Maroon">c<sub>9</sub></font> = <font color="Maroon">c<sub>8</sub></font> as    <a href="scmfsa_2.html#M2">FinSeq-Location</a>  <b>by </b><i><a class="ref" href="scmfsa_2.html#T12">SCMFSA_2:12</a></i>;<br/><b>thus </b><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>8</sub></font> = 
<font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>9</sub></font>
<b>by </b><i><a class="txt" href="sfmastr2.html#E7:6"><i><font color="Green">E11</font></i></a>, <a class="txt" href="sfmastr2.html#E2:6_2"><i><font color="Green">E12</font></i></a></i>
<br/>.= 
<font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>8</sub></font>

;<br/></div><b>end;</b></div>
<a NAME="E9:6"/><b>then </b>
( <font color="Maroon">c<sub>4</sub></font> <a href="relat_1.html#K7">|</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="relat_1.html#K7">|</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="relat_1.html#K7">|</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="relat_1.html#K7">|</a> <font color="Maroon">c<sub>7</sub></font> )
 
<b>by </b><i><a class="txt" href="sfmastr2.html#E3:6"><i><font color="Green">E8</font></i></a>, <a class="txt" href="sfmastr2.html#E4:6"><i><font color="Green">E9</font></i></a>, <a class="ref" href="scmfsa6a.html#T9">SCMFSA6A:9</a></i>;<br/>
<b>hence </b><a NAME="E10:6"/>
<font color="Maroon">c<sub>4</sub></font> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="relat_1.html#T185">RELAT_1:185</a></i>;<br/>


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