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<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">y</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">c</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">s</font> be   <a href="circuit1.html#NM3">State</a> of <span class="p1">(<span class="default"><a href="fscirc_1.html#K7">BorrowCirc</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">c</font></span>)</span>;<br/><b>let </b><font color="Maroon">a1</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="circcomb.html#K10">BOOLEAN</a> , <font color="Maroon">a2</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="circcomb.html#K10">BOOLEAN</a> , <font color="Maroon">a3</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="circcomb.html#K10">BOOLEAN</a> ;<br/>





<b>assume </b><a NAME="E1:27"/><i><font color="Green">E28</font></i>: 
( <font color="Maroon">a1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> &amp; <font color="Maroon">a2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">y</font> &amp; <font color="Maroon">a3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c</font> )
 ;<br/>

<b>set </b><font color="Maroon">S</font> =  <a href="fscirc_1.html#K4">BorrowStr</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">c</font>;<br/>
<a NAME="E2:27"/><i><font color="Green">E44</font></i>: 
 <a href="msafree2.html#K4">InnerVertices</a> <span class="p1">(<span class="default"><a href="fscirc_1.html#K4">BorrowStr</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">c</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="fscirc_1.html#K4">BorrowStr</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">c</font></span>)</span>
 
<b>by </b><i><a class="ref" href="facirc_1.html#T37">FACIRC_1:37</a></i>;<br/>
<a NAME="E3:27"/><i><font color="Green">E45</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">s</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="fscirc_1.html#K4">BorrowStr</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">c</font></span>)</span>
 
<b>by </b><i><a class="ref" href="circuit1.html#T4">CIRCUIT1:4</a></i>;<br/>
<a NAME="E4:27"/><i><font color="Green">E46</font></i>: 
( <font color="Maroon">x</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="fscirc_1.html#K4">BorrowStr</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">c</font></span>)</span> &amp; <font color="Maroon">y</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="fscirc_1.html#K4">BorrowStr</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">c</font></span>)</span> &amp; <font color="Maroon">c</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="fscirc_1.html#K4">BorrowStr</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">c</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="fscirc_1.html#T6">FSCIRC_1:6</a></i>;<br/>
<a NAME="E5:27"/>
<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">x</font>,<font color="Maroon">y</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="fscirc_1.html#K4">BorrowStr</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">c</font></span>)</span>
 
<b>by </b><i><a class="ref" href="fscirc_1.html#T7">FSCIRC_1:7</a></i>;<br/>
<b>hence </b><span class="p1">(<span class="default"><a href="circuit2.html#K6">Following</a> <font color="Maroon">s</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">x</font>,<font color="Maroon">y</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">s</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">x</font>,<font color="Maroon">y</font></span><a href="facirc_1.html#K6">*&gt;</a></span></span>)</span>
<b>by </b><i>, <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">a1</font>,<font color="Maroon">a2</font></span><a href="facirc_1.html#K6">*&gt;</a></span>
<b>by </b><i>, , , <a class="ref" href="finseq_2.html#T145">FINSEQ_2:145</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="margrel1.html#K9">'not'</a> <font color="Maroon">a1</font></span>)</span> <a href="margrel1.html#K10">'&amp;'</a> <font color="Maroon">a2</font>
<b>by </b><i><a class="ref" href="twoscomp.html#D2">TWOSCOMP:def 2</a></i>
;<br/><br/>

<a NAME="E7:27"/>
<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">y</font>,<font color="Maroon">c</font></span><a href="facirc_1.html#K6">*&gt;</a></span>,<a href="twoscomp.html#K2">and2</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="fscirc_1.html#K4">BorrowStr</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">c</font></span>)</span>
 
<b>by </b><i><a class="ref" href="fscirc_1.html#T7">FSCIRC_1:7</a></i>;<br/>
<b>hence </b><span class="p1">(<span class="default"><a href="circuit2.html#K6">Following</a> <font color="Maroon">s</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">y</font>,<font color="Maroon">c</font></span><a href="facirc_1.html#K6">*&gt;</a></span>,<a href="twoscomp.html#K2">and2</a> </span><a href="tarski.html#K4">]</a></span> = 
<a href="twoscomp.html#K2">and2</a>  <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">s</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">y</font>,<font color="Maroon">c</font></span><a href="facirc_1.html#K6">*&gt;</a></span></span>)</span>
<b>by </b><i>, <a class="ref" href="facirc_1.html#T35">FACIRC_1:35</a></i>
<br/>.= 
<a href="twoscomp.html#K2">and2</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">a2</font>,<font color="Maroon">a3</font></span><a href="facirc_1.html#K6">*&gt;</a></span>
<b>by </b><i>, , , <a class="ref" href="finseq_2.html#T145">FINSEQ_2:145</a></i>
<br/>.= 
<font color="Maroon">a2</font> <a href="margrel1.html#K10">'&amp;'</a> <font color="Maroon">a3</font>
<b>by </b><i><a class="ref" href="twoscomp.html#D1">TWOSCOMP:def 1</a></i>
;<br/><br/>

<a NAME="E9:27"/>
<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">x</font>,<font color="Maroon">c</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="fscirc_1.html#K4">BorrowStr</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">c</font></span>)</span>
 
<b>by </b><i><a class="ref" href="fscirc_1.html#T7">FSCIRC_1:7</a></i>;<br/>
<b>hence </b><span class="p1">(<span class="default"><a href="circuit2.html#K6">Following</a> <font color="Maroon">s</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">x</font>,<font color="Maroon">c</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">s</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">x</font>,<font color="Maroon">c</font></span><a href="facirc_1.html#K6">*&gt;</a></span></span>)</span>
<b>by </b><i>, <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">a1</font>,<font color="Maroon">a3</font></span><a href="facirc_1.html#K6">*&gt;</a></span>
<b>by </b><i>, , , <a class="ref" href="finseq_2.html#T145">FINSEQ_2:145</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="margrel1.html#K9">'not'</a> <font color="Maroon">a1</font></span>)</span> <a href="margrel1.html#K10">'&amp;'</a> <font color="Maroon">a3</font>
<b>by </b><i><a class="ref" href="twoscomp.html#D2">TWOSCOMP:def 2</a></i>
;<br/><br/>


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