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<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">y</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">f</font> be   <a href="funct_2.html#NM1">Function</a> of 2 <a href="finseq_2.html#K4">-tuples_on</a> <a href="circcomb.html#K10">BOOLEAN</a> , <a href="circcomb.html#K10">BOOLEAN</a> ;<br/>







<b>set </b><font color="Maroon">p</font> = <span class="p1"><a href="facirc_1.html#K6" target="_self">&lt;*</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><span class="p3"><a href="facirc_1.html#K6" target="_self">&lt;*</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="facirc_1.html#K6" target="_self">*&gt;</a></span>,<font color="Maroon">f</font></span><a href="tarski.html#K4">]</a></span>,<font color="Maroon">c</font></span><a href="facirc_1.html#K6" target="_self">*&gt;</a></span>;<br/>
<b>set </b><font color="Maroon">S1</font> =  <a href="circcomb.html#K7">1GateCircStr</a> <span class="p1"><a href="facirc_1.html#K6" target="_self">&lt;*</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="facirc_1.html#K6" target="_self">*&gt;</a></span>,<font color="Maroon">f</font>;<br/>
<b>set </b><font color="Maroon">S2</font> =  <a href="circcomb.html#K7">1GateCircStr</a> <span class="p1"><a href="facirc_1.html#K6" target="_self">&lt;*</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><span class="p3"><a href="facirc_1.html#K6" target="_self">&lt;*</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="facirc_1.html#K6" target="_self">*&gt;</a></span>,<font color="Maroon">f</font></span><a href="tarski.html#K4">]</a></span>,<font color="Maroon">c</font></span><a href="facirc_1.html#K6" target="_self">*&gt;</a></span>,<font color="Maroon">f</font>;<br/>
<b>set </b><font color="Maroon">S</font> =  <a href="facirc_1.html#K12" target="_self">2GatesCircStr</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">c</font>,<font color="Maroon">f</font>;<br/>
<a NAME="E1:89"/>
(  <a href="facirc_1.html#K12" target="_self">2GatesCircStr</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">c</font>,<font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="circcomb.html#K7">1GateCircStr</a> <span class="p2"><a href="facirc_1.html#K6" target="_self">&lt;*</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="facirc_1.html#K6" target="_self">*&gt;</a></span>,<font color="Maroon">f</font></span>)</span> <a href="circcomb.html#K3">+*</a> <span class="p1">(<span class="default"><a href="circcomb.html#K7">1GateCircStr</a> <span class="p2"><a href="facirc_1.html#K6" target="_self">&lt;*</a><span class="default"><span class="p3"><a href="tarski.html#K4">[</a><span class="default"><span class="p4"><a href="facirc_1.html#K6" target="_self">&lt;*</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="facirc_1.html#K6" target="_self">*&gt;</a></span>,<font color="Maroon">f</font></span><a href="tarski.html#K4">]</a></span>,<font color="Maroon">c</font></span><a href="facirc_1.html#K6" target="_self">*&gt;</a></span>,<font color="Maroon">f</font></span>)</span> &amp;  <a href="circcomb.html#K7">1GateCircStr</a> <span class="p1"><a href="facirc_1.html#K6" target="_self">&lt;*</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="facirc_1.html#K6" target="_self">*&gt;</a></span>,<font color="Maroon">f</font> <a href="circcomb.html#R1">tolerates</a>  <a href="circcomb.html#K7">1GateCircStr</a> <span class="p1"><a href="facirc_1.html#K6" target="_self">&lt;*</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><span class="p3"><a href="facirc_1.html#K6" target="_self">&lt;*</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="facirc_1.html#K6" target="_self">*&gt;</a></span>,<font color="Maroon">f</font></span><a href="tarski.html#K4">]</a></span>,<font color="Maroon">c</font></span><a href="facirc_1.html#K6" target="_self">*&gt;</a></span>,<font color="Maroon">f</font> )
 
<b>by </b><i><a class="ref" href="circcomb.html#T51">CIRCCOMB:51</a></i>;<br/>
<b>hence </b> <a href="msafree2.html#K4">InnerVertices</a> <span class="p1">(<span class="default"><a href="facirc_1.html#K12" target="_self">2GatesCircStr</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">c</font>,<font color="Maroon">f</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="msafree2.html#K4">InnerVertices</a> <span class="p2">(<span class="default"><a href="circcomb.html#K7">1GateCircStr</a> <span class="p3"><a href="facirc_1.html#K6" target="_self">&lt;*</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="facirc_1.html#K6" target="_self">*&gt;</a></span>,<font color="Maroon">f</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="msafree2.html#K4">InnerVertices</a> <span class="p2">(<span class="default"><a href="circcomb.html#K7">1GateCircStr</a> <span class="p3"><a href="facirc_1.html#K6" target="_self">&lt;*</a><span class="default"><span class="p4"><a href="tarski.html#K4">[</a><span class="default"><span class="p5"><a href="facirc_1.html#K6" target="_self">&lt;*</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="facirc_1.html#K6" target="_self">*&gt;</a></span>,<font color="Maroon">f</font></span><a href="tarski.html#K4">]</a></span>,<font color="Maroon">c</font></span><a href="facirc_1.html#K6" target="_self">*&gt;</a></span>,<font color="Maroon">f</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="circcomb.html#T15">CIRCCOMB:15</a></i>
<br/>.= 
<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><span class="p3"><a href="facirc_1.html#K6" target="_self">&lt;*</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="facirc_1.html#K6" target="_self">*&gt;</a></span>,<font color="Maroon">f</font></span><a href="tarski.html#K4">]</a></span></span><a href="tarski.html#K1">}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="msafree2.html#K4">InnerVertices</a> <span class="p2">(<span class="default"><a href="circcomb.html#K7">1GateCircStr</a> <span class="p3"><a href="facirc_1.html#K6" target="_self">&lt;*</a><span class="default"><span class="p4"><a href="tarski.html#K4">[</a><span class="default"><span class="p5"><a href="facirc_1.html#K6" target="_self">&lt;*</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="facirc_1.html#K6" target="_self">*&gt;</a></span>,<font color="Maroon">f</font></span><a href="tarski.html#K4">]</a></span>,<font color="Maroon">c</font></span><a href="facirc_1.html#K6" target="_self">*&gt;</a></span>,<font color="Maroon">f</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="circcomb.html#T49">CIRCCOMB:49</a></i>
<br/>.= 
<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><span class="p3"><a href="facirc_1.html#K6" target="_self">&lt;*</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="facirc_1.html#K6" target="_self">*&gt;</a></span>,<font color="Maroon">f</font></span><a href="tarski.html#K4">]</a></span></span><a href="tarski.html#K1">}</a></span> <a href="xboole_0.html#K2">\/</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"><span class="p3"><a href="facirc_1.html#K6" target="_self">&lt;*</a><span class="default"><span class="p4"><a href="tarski.html#K4">[</a><span class="default"><span class="p5"><a href="facirc_1.html#K6" target="_self">&lt;*</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="facirc_1.html#K6" target="_self">*&gt;</a></span>,<font color="Maroon">f</font></span><a href="tarski.html#K4">]</a></span>,<font color="Maroon">c</font></span><a href="facirc_1.html#K6" target="_self">*&gt;</a></span>,<font color="Maroon">f</font></span><a href="tarski.html#K4">]</a></span></span><a href="tarski.html#K1">}</a></span>
<b>by </b><i><a class="ref" href="circcomb.html#T49">CIRCCOMB:49</a></i>
<br/>.= 
<span class="p1"><a href="tarski.html#K2">{</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><span class="p3"><a href="facirc_1.html#K6" target="_self">&lt;*</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="facirc_1.html#K6" target="_self">*&gt;</a></span>,<font color="Maroon">f</font></span><a href="tarski.html#K4">]</a></span>,<span class="p2">(<span class="default"><a href="facirc_1.html#K13" target="_self">2GatesCircOutput</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">c</font>,<font color="Maroon">f</font></span>)</span></span><a href="tarski.html#K2">}</a></span>
<b>by </b><i><a class="ref" href="enumset1.html#T41">ENUMSET1:41</a></i>
;<br/><br/>


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