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<div class="add">

<b>set </b><font color="Maroon">c<sub>1</sub></font> =  <a href="twoscomp.html#K3">and2a</a> ;<br/>
<b>set </b><font color="Maroon">c<sub>2</sub></font> =  <a href="gfacirc1.html#K3" target="_self">and2c</a> ;<br/>
<b>set </b><font color="Maroon">c<sub>3</sub></font> =  <a href="twoscomp.html#K4">and2b</a> ;<br/>
<b>let </b><font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>6</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>7</sub></font> be   <a href="circuit1.html#NM3">State</a> of <span class="p1">(<span class="default"><a href="gfacirc1.html#K32" target="_self">GFA2CarryCirc</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span>;<br/>



<b>set </b><font color="Maroon">c<sub>8</sub></font> = <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2"><a href="facirc_1.html#K6">&lt;*</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span><a href="facirc_1.html#K6">*&gt;</a></span>,<a href="twoscomp.html#K3">and2a</a> </span><a href="tarski.html#K4">]</a></span>;<br/>
<b>set </b><font color="Maroon">c<sub>9</sub></font> = <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2"><a href="facirc_1.html#K6">&lt;*</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span><a href="facirc_1.html#K6">*&gt;</a></span>,<a href="gfacirc1.html#K3" target="_self">and2c</a> </span><a href="tarski.html#K4">]</a></span>;<br/>
<b>set </b><font color="Maroon">c<sub>10</sub></font> = <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2"><a href="facirc_1.html#K6">&lt;*</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="facirc_1.html#K6">*&gt;</a></span>,<a href="twoscomp.html#K4">and2b</a> </span><a href="tarski.html#K4">]</a></span>;<br/>
<b>let </b><font color="Maroon">c<sub>11</sub></font>, <font color="Maroon">c<sub>12</sub></font>, <font color="Maroon">c<sub>13</sub></font> be    <a href="subset_1.html#M1">Element</a> of  <a href="circcomb.html#K10">BOOLEAN</a> ;<br/>

<b>assume </b><a NAME="E1:121"/><i><font color="Green">E73</font></i>: 
( <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font> )
 ;<br/>

<b>set </b><font color="Maroon">c<sub>14</sub></font> =  <a href="gfacirc1.html#K31" target="_self">GFA2CarryStr</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>;<br/>
<a NAME="E2:121"/><i><font color="Green">E74</font></i>: 
 <a href="msafree2.html#K4">InnerVertices</a> <span class="p1">(<span class="default"><a href="gfacirc1.html#K31" target="_self">GFA2CarryStr</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <span class="p1">(<span class="default"><a href="gfacirc1.html#K31" target="_self">GFA2CarryStr</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="facirc_1.html#T37">FACIRC_1:37</a></i>;<br/>
<a NAME="E3:121"/><i><font color="Green">E75</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="gfacirc1.html#K31" target="_self">GFA2CarryStr</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="circuit1.html#T4">CIRCUIT1:4</a></i>;<br/>
<a NAME="E4:121"/><i><font color="Green">E76</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="gfacirc1.html#K31" target="_self">GFA2CarryStr</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="gfacirc1.html#K31" target="_self">GFA2CarryStr</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="gfacirc1.html#K31" target="_self">GFA2CarryStr</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> )
 
<b>by </b><i><a class="ref" href="gfacirc1.html#T92" target="_self">Th92</a></i>;<br/>
<a NAME="E5:121"/>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2"><a href="facirc_1.html#K6">&lt;*</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span><a href="facirc_1.html#K6">*&gt;</a></span>,<a href="twoscomp.html#K3">and2a</a> </span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="msafree2.html#K4">InnerVertices</a> <span class="p1">(<span class="default"><a href="gfacirc1.html#K31" target="_self">GFA2CarryStr</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="gfacirc1.html#T93" target="_self">Th93</a></i>;<br/>
<b>hence </b><span class="p1">(<span class="default"><a href="circuit2.html#K6">Following</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2"><a href="facirc_1.html#K6">&lt;*</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span><a href="facirc_1.html#K6">*&gt;</a></span>,<a href="twoscomp.html#K3">and2a</a> </span><a href="tarski.html#K4">]</a></span> = 
<a href="twoscomp.html#K3">and2a</a>  <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2"><a href="facirc_1.html#K6">&lt;*</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span><a href="facirc_1.html#K6">*&gt;</a></span></span>)</span>
<b>by </b><i><a class="txt" href="gfacirc1.html#E2:121"><i><font color="Green">E74</font></i></a>, <a class="ref" href="facirc_1.html#T35">FACIRC_1:35</a></i>
<br/>.= 
<a href="twoscomp.html#K3">and2a</a>  <a href="funct_1.html#K1">.</a> <span class="p1"><a href="facirc_1.html#K6">&lt;*</a><span class="default"><font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>12</sub></font></span><a href="facirc_1.html#K6">*&gt;</a></span>
<b>by </b><i><a class="txt" href="gfacirc1.html#E1:121"><i><font color="Green">E73</font></i></a>, <a class="txt" href="gfacirc1.html#E3:121"><i><font color="Green">E75</font></i></a>, <a class="txt" href="gfacirc1.html#E4:121"><i><font color="Green">E76</font></i></a>, <a class="ref" href="finseq_2.html#T145">FINSEQ_2:145</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="margrel1.html#K11">'not'</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="margrel1.html#K12">'&amp;'</a> <font color="Maroon">c<sub>12</sub></font>
<b>by </b><i><a class="ref" href="twoscomp.html#D2">TWOSCOMP:def 2</a></i>
;<br/><br/>

<a NAME="E7:121"/>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2"><a href="facirc_1.html#K6">&lt;*</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span><a href="facirc_1.html#K6">*&gt;</a></span>,<a href="gfacirc1.html#K3" target="_self">and2c</a> </span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="msafree2.html#K4">InnerVertices</a> <span class="p1">(<span class="default"><a href="gfacirc1.html#K31" target="_self">GFA2CarryStr</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="gfacirc1.html#T93" target="_self">Th93</a></i>;<br/>
<b>hence </b><span class="p1">(<span class="default"><a href="circuit2.html#K6">Following</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2"><a href="facirc_1.html#K6">&lt;*</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span><a href="facirc_1.html#K6">*&gt;</a></span>,<a href="gfacirc1.html#K3" target="_self">and2c</a> </span><a href="tarski.html#K4">]</a></span> = 
<a href="gfacirc1.html#K3" target="_self">and2c</a>  <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2"><a href="facirc_1.html#K6">&lt;*</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span><a href="facirc_1.html#K6">*&gt;</a></span></span>)</span>
<b>by </b><i><a class="txt" href="gfacirc1.html#E2:121"><i><font color="Green">E74</font></i></a>, <a class="ref" href="facirc_1.html#T35">FACIRC_1:35</a></i>
<br/>.= 
<a href="gfacirc1.html#K3" target="_self">and2c</a>  <a href="funct_1.html#K1">.</a> <span class="p1"><a href="facirc_1.html#K6">&lt;*</a><span class="default"><font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>13</sub></font></span><a href="facirc_1.html#K6">*&gt;</a></span>
<b>by </b><i><a class="txt" href="gfacirc1.html#E1:121"><i><font color="Green">E73</font></i></a>, <a class="txt" href="gfacirc1.html#E3:121"><i><font color="Green">E75</font></i></a>, <a class="txt" href="gfacirc1.html#E4:121"><i><font color="Green">E76</font></i></a>, <a class="ref" href="finseq_2.html#T145">FINSEQ_2:145</a></i>
<br/>.= 
<font color="Maroon">c<sub>12</sub></font> <a href="margrel1.html#K12">'&amp;'</a> <span class="p1">(<span class="default"><a href="margrel1.html#K11">'not'</a> <font color="Maroon">c<sub>13</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="gfacirc1.html#D3" target="_self">Def3</a></i>
;<br/><br/>

<a NAME="E9:121"/>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2"><a href="facirc_1.html#K6">&lt;*</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="facirc_1.html#K6">*&gt;</a></span>,<a href="twoscomp.html#K4">and2b</a> </span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="msafree2.html#K4">InnerVertices</a> <span class="p1">(<span class="default"><a href="gfacirc1.html#K31" target="_self">GFA2CarryStr</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="gfacirc1.html#T93" target="_self">Th93</a></i>;<br/>
<b>hence </b><span class="p1">(<span class="default"><a href="circuit2.html#K6">Following</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2"><a href="facirc_1.html#K6">&lt;*</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="facirc_1.html#K6">*&gt;</a></span>,<a href="twoscomp.html#K4">and2b</a> </span><a href="tarski.html#K4">]</a></span> = 
<a href="twoscomp.html#K4">and2b</a>  <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2"><a href="facirc_1.html#K6">&lt;*</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="facirc_1.html#K6">*&gt;</a></span></span>)</span>
<b>by </b><i><a class="txt" href="gfacirc1.html#E2:121"><i><font color="Green">E74</font></i></a>, <a class="ref" href="facirc_1.html#T35">FACIRC_1:35</a></i>
<br/>.= 
<a href="twoscomp.html#K4">and2b</a>  <a href="funct_1.html#K1">.</a> <span class="p1"><a href="facirc_1.html#K6">&lt;*</a><span class="default"><font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="facirc_1.html#K6">*&gt;</a></span>
<b>by </b><i><a class="txt" href="gfacirc1.html#E1:121"><i><font color="Green">E73</font></i></a>, <a class="txt" href="gfacirc1.html#E3:121"><i><font color="Green">E75</font></i></a>, <a class="txt" href="gfacirc1.html#E4:121"><i><font color="Green">E76</font></i></a>, <a class="ref" href="finseq_2.html#T145">FINSEQ_2:145</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="margrel1.html#K11">'not'</a> <font color="Maroon">c<sub>13</sub></font></span>)</span> <a href="margrel1.html#K12">'&amp;'</a> <span class="p1">(<span class="default"><a href="margrel1.html#K11">'not'</a> <font color="Maroon">c<sub>11</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="twoscomp.html#D3">TWOSCOMP:def 3</a></i>
;<br/><br/>


</div>
