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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be  non <a href="xboole_0.html#V1">empty</a> <a href="finset_1.html#V1">finite</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">c<sub>1</sub></font> <a href="finseq_2.html#K4">-tuples_on</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>2</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be    <a href="circcomb.html#M1">FinSeqLen</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>5</sub></font> be    <a href="circcmb3.html#M1" target="_self">Signature</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>









<b>assume </b><b>that </b><br/><a NAME="E1:82"/><i><font color="Green">E38</font></i>: 
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>4</sub></font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>5</sub></font>
 <b>and </b><br/><a NAME="E2:82"/><i><font color="Green">E39</font></i>: 
not  <a href="circcmb3.html#K5" target="_self">Output</a> <span class="p1">(<span class="default"><a href="circcmb3.html#K6" target="_self">1GateCircStr</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="msafree2.html#K2">InputVertices</a> <font color="Maroon">c<sub>5</sub></font>
 ;<br/>

<a NAME="E3:82"/>
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="msafree2.html#K2">InputVertices</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><a href="msafree2.html#K4">InnerVertices</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T45">XBOOLE_1:45</a></i>;<br/>
<a NAME="E4:82"/><b>then </b><i><font color="Green">E40</font></i>: 
<span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p1">(<span class="default"><a href="msafree2.html#K4">InnerVertices</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="msafree2.html#K2">InputVertices</a> <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="circcmb3.html#E1:82"><i><font color="Green">E38</font></i></a>, <a class="ref" href="xboole_1.html#T43">XBOOLE_1:43</a></i>;<br/>
<a NAME="E5:82"/>
<font color="Maroon">c<sub>5</sub></font> <a href="circcomb.html#R1">tolerates</a>  <a href="circcmb3.html#K6" target="_self">1GateCircStr</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="circcomb.html#T55">CIRCCOMB:55</a></i>;<br/>
<b>hence </b> <a href="msafree2.html#K2">InputVertices</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="circcmb3.html#K8" target="_self">+*</a> <span class="p2">(<span class="default"><a href="circcmb3.html#K6" target="_self">1GateCircStr</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msafree2.html#K2">InputVertices</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2">(<span class="default"><a href="msafree2.html#K4">InnerVertices</a> <span class="p3">(<span class="default"><a href="circcmb3.html#K6" target="_self">1GateCircStr</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msafree2.html#K2">InputVertices</a> <span class="p3">(<span class="default"><a href="circcmb3.html#K6" target="_self">1GateCircStr</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2">(<span class="default"><a href="msafree2.html#K4">InnerVertices</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="circcmb2.html#T6">CIRCCMB2:6</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msafree2.html#K2">InputVertices</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2">(<span class="default"><a href="msafree2.html#K4">InnerVertices</a> <span class="p3">(<span class="default"><a href="circcmb3.html#K6" target="_self">1GateCircStr</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p2">(<span class="default"><a href="msafree2.html#K4">InnerVertices</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="circcomb.html#T49">CIRCCOMB:49</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msafree2.html#K2">InputVertices</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="circcmb3.html#K5" target="_self">Output</a> <span class="p4">(<span class="default"><a href="circcmb3.html#K6" target="_self">1GateCircStr</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p2">(<span class="default"><a href="msafree2.html#K4">InnerVertices</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="circcmb3.html#T17" target="_self">Th17</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="msafree2.html#K2">InputVertices</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p2">(<span class="default"><a href="msafree2.html#K4">InnerVertices</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="circcmb3.html#E2:82"><i><font color="Green">E39</font></i></a>, <a class="ref" href="zfmisc_1.html#T65">ZFMISC_1:65</a></i>
<br/>.= 
 <a href="msafree2.html#K2">InputVertices</a> <font color="Maroon">c<sub>5</sub></font>
<b>by </b><i><a class="txt" href="circcmb3.html#E4:82"><i><font color="Green">E40</font></i></a>, <a class="ref" href="xboole_1.html#T12">XBOOLE_1:12</a></i>
;<br/><br/>


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