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<b>let </b><font color="Maroon">f</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">p</font> be   <a href="finseq_1.html#NM1">FinSequence</a>;<br/>



<a NAME="E1:60"/>
( not the <a href="msualg_1.html#U1">OperSymbols</a> of <span class="p1">(<span class="default"><a href="circcomb.html#K6" target="_self">1GateCircStr</a> <font color="Maroon">p</font>,<font color="Maroon">f</font>,<font color="Maroon">x</font></span>)</span> is <a href="xboole_0.html#V1">empty</a> &amp; the <a href="msualg_1.html#U3">ResultSort</a> of <span class="p1">(<span class="default"><a href="circcomb.html#K6" target="_self">1GateCircStr</a> <font color="Maroon">p</font>,<font color="Maroon">f</font>,<font color="Maroon">x</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">p</font>,<font color="Maroon">f</font></span><a href="tarski.html#K4">]</a></span></span><a href="tarski.html#K1">}</a></span> <a href="pre_circ.html#K2">--&gt;</a> <font color="Maroon">x</font> )
 
<b>by </b><i><a class="ref" href="circcomb.html#T2" target="_self">Th2</a>, <a class="ref" href="msualg_1.html#D5">MSUALG_1:def 5</a></i>;<br/>
<a NAME="E2:60"/><b>then </b><i><font color="Green">E24</font></i>: 
 <a href="relat_1.html#K2">rng</a> the <a href="msualg_1.html#U3">ResultSort</a> of <span class="p1">(<span class="default"><a href="circcomb.html#K6" target="_self">1GateCircStr</a> <font color="Maroon">p</font>,<font color="Maroon">f</font>,<font color="Maroon">x</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x</font></span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i><a class="ref" href="funcop_1.html#T14">FUNCOP_1:14</a></i>;<br/>
<a NAME="E3:60"/>
the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="circcomb.html#K6" target="_self">1GateCircStr</a> <font color="Maroon">p</font>,<font color="Maroon">f</font>,<font color="Maroon">x</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">p</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x</font></span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i/>;<br/>
<a NAME="E4:60"/><b>then </b>
 <a href="msafree2.html#K2">InputVertices</a> <span class="p1">(<span class="default"><a href="circcomb.html#K6" target="_self">1GateCircStr</a> <font color="Maroon">p</font>,<font color="Maroon">f</font>,<font color="Maroon">x</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">p</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x</font></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x</font></span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E5:60"/>
(  <a href="msafree2.html#K2">InputVertices</a> <span class="p1">(<span class="default"><a href="circcomb.html#K6" target="_self">1GateCircStr</a> <font color="Maroon">p</font>,<font color="Maroon">f</font>,<font color="Maroon">x</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">p</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x</font></span><a href="tarski.html#K1">}</a></span> &amp;  <a href="msafree2.html#K4">InnerVertices</a> <span class="p1">(<span class="default"><a href="circcomb.html#K6" target="_self">1GateCircStr</a> <font color="Maroon">p</font>,<font color="Maroon">f</font>,<font color="Maroon">x</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x</font></span><a href="tarski.html#K1">}</a></span> )
 <b>by </b><i>, <a class="ref" href="xboole_1.html#T40">XBOOLE_1:40</a></i>;<br/>


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