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<b>let </b><font color="Maroon" title="c1">x</font>, <font color="Maroon" title="c2">y</font>, <font color="Maroon" title="c3">c</font> be  non <a href="facirc_1.html#V1" title="FACIRC_1:attr.1">pair</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c4">s</font> be   <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <span class="p1">(<span class="default"><a href="fscirc_1.html#K7" title="FSCIRC_1:func.7">BorrowCirc</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">c</font></span>)</span>;<br/><b>let </b><font color="Maroon" title="c5">a1</font>, <font color="Maroon" title="c6">a2</font>, <font color="Maroon" title="c7">a3</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="circcomb.html#K10" title="CIRCCOMB:func.10">BOOLEAN</a> ;<br/>





<b>assume </b><a NAME="E1:21"/><i><font color="Green" title="E9">A1</font></i>: 
( <font color="Maroon" title="c5">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K3" title="TWOSCOMP:func.3">and2a</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> &amp; <font color="Maroon" title="c6">a2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">c</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K2" title="TWOSCOMP:func.2">and2</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> &amp; <font color="Maroon" title="c7">a3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c3">c</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K3" title="TWOSCOMP:func.3">and2a</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> )
 ;<br/>

<b>set </b><font color="Maroon" title="c8">xy</font> = <span class="p1"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>;<br/>
<b>set </b><font color="Maroon" title="c9">yc</font> = <span class="p1"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">c</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>;<br/>
<b>set </b><font color="Maroon" title="c10">xc</font> = <span class="p1"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c3">c</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>;<br/>
<b>set </b><font color="Maroon" title="c11">xy1</font> = <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K3" title="TWOSCOMP:func.3">and2a</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>;<br/>
<b>set </b><font color="Maroon" title="c12">yc1</font> = <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">c</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K2" title="TWOSCOMP:func.2">and2</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>;<br/>
<b>set </b><font color="Maroon" title="c13">xc1</font> = <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c3">c</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K3" title="TWOSCOMP:func.3">and2a</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>;<br/>
<b>set </b><font color="Maroon" title="c14">S</font> =  <a href="fscirc_1.html#K4" title="FSCIRC_1:func.4">BorrowStr</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">c</font>;<br/>
<a NAME="E2:21"/><i><font color="Green" title="E10">A2</font></i>: 
 <a href="msafree2.html#K4" title="MSAFREE2:func.4">InnerVertices</a> <span class="p1">(<span class="default"><a href="fscirc_1.html#K4" title="FSCIRC_1:func.4">BorrowStr</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">c</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">OperSymbols</a> of <span class="p1">(<span class="default"><a href="fscirc_1.html#K4" title="FSCIRC_1:func.4">BorrowStr</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">c</font></span>)</span>
 
<b>by </b><i><a class="ref" href="facirc_1.html#T37" title="FACIRC_1:th.37">FACIRC_1:37</a></i>;<br/>
<a NAME="E3:21"/><i><font color="Green" title="E11">A3</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c4">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="fscirc_1.html#K4" title="FSCIRC_1:func.4">BorrowStr</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">c</font></span>)</span>
 
<b>by </b><i><a class="ref" href="circuit1.html#T4" title="CIRCUIT1:th.4">CIRCUIT1:4</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c15">xy1</font> = <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K3" title="TWOSCOMP:func.3">and2a</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>, <font color="Maroon" title="c16">yc1</font> = <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">c</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K2" title="TWOSCOMP:func.2">and2</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>, <font color="Maroon" title="c17">xc1</font> = <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c3">c</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K3" title="TWOSCOMP:func.3">and2a</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="msafree2.html#K4" title="MSAFREE2:func.4">InnerVertices</a> <span class="p1">(<span class="default"><a href="fscirc_1.html#K4" title="FSCIRC_1:func.4">BorrowStr</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">c</font></span>)</span> <b>by </b><i><a class="ref" href="fscirc_1.html#T7" target="_self" title="FSCIRC_1:th.7">Th7</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><a href="circuit2.html#K6" title="CIRCUIT2:func.6">Following</a> <font color="Maroon" title="c4">s</font></span>)</span> <a href="facirc_1.html#K15" title="FACIRC_1:func.15">.</a> <span class="p1">(<span class="default"><a href="fscirc_1.html#K6" title="FSCIRC_1:func.6">BorrowOutput</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">c</font></span>)</span> = 
<a href="facirc_1.html#K4" title="FACIRC_1:func.4">or3</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2"><a href="facirc_1.html#K7" title="FACIRC_1:func.7">&lt;*</a><span class="default"><font color="Maroon" title="c15">xy1</font>,<font color="Maroon" title="c16">yc1</font>,<font color="Maroon" title="c17">xc1</font></span><a href="facirc_1.html#K7" title="FACIRC_1:func.7">*&gt;</a></span></span>)</span>
<b>by </b><i><a class="txt" href="fscirc_1.html#E2:21"><i><font color="Green" title="E10">A2</font></i></a>, <a class="ref" href="facirc_1.html#T35" title="FACIRC_1:th.35">FACIRC_1:35</a></i>
<br/>.= 
<a href="facirc_1.html#K4" title="FACIRC_1:func.4">or3</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="facirc_1.html#K7" title="FACIRC_1:func.7">&lt;*</a><span class="default"><font color="Maroon" title="c5">a1</font>,<font color="Maroon" title="c6">a2</font>,<font color="Maroon" title="c7">a3</font></span><a href="facirc_1.html#K7" title="FACIRC_1:func.7">*&gt;</a></span>
<b>by </b><i><a class="txt" href="fscirc_1.html#E1:21"><i><font color="Green" title="E9">A1</font></i></a>, <a class="txt" href="fscirc_1.html#E3:21"><i><font color="Green" title="E11">A3</font></i></a>, <a class="ref" href="finseq_2.html#T146" title="FINSEQ_2:th.146">FINSEQ_2:146</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">a1</font> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <font color="Maroon" title="c6">a2</font></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <font color="Maroon" title="c7">a3</font>
<b>by </b><i><a class="ref" href="facirc_1.html#D7" title="FACIRC_1:def.7">FACIRC_1:def 7</a></i>
;<br/>


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