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<b>let </b><font color="Maroon" title="c1">x1</font>, <font color="Maroon" title="c2">x2</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c3">X</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c4">n</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>let </b><font color="Maroon" title="c5">f</font> be   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c4">n</font> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <font color="Maroon" title="c3">X</font>,<font color="Maroon" title="c3">X</font>;<br/><b>let </b><font color="Maroon" title="c6">p</font> be    <a href="circcomb.html#M1" title="CIRCCOMB:mode.1">FinSeqLen</a> of <font color="Maroon" title="c4">n</font>;<br/><b>let </b><font color="Maroon" title="c7">S</font> be    <a href="circcmb3.html#M1" title="CIRCCMB3:mode.1">Signature</a> of <font color="Maroon" title="c3">X</font>;<br/>











<b>assume </b><b>that </b><br/><a NAME="E1:83"/><i><font color="Green" title="E39">A1</font></i>: 
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c6">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">x1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">x2</font>
 <b>and </b><br/><a NAME="E2:83"/><i><font color="Green" title="E40">A2</font></i>: 
( <font color="Maroon" title="c1">x1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c7">S</font> &amp; <font color="Maroon" title="c2">x2</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="msafree2.html#K4" title="MSAFREE2:func.4">InnerVertices</a> <font color="Maroon" title="c7">S</font> )
 <b>and </b><br/><a NAME="E3:83"/><i><font color="Green" title="E41">A3</font></i>: 
not  <a href="circcmb3.html#K5" title="CIRCCMB3:func.5">Output</a> <span class="p1">(<span class="default"><a href="circcmb3.html#K6" title="CIRCCMB3:func.6">1GateCircStr</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c5">f</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="msafree2.html#K2" title="MSAFREE2:func.2">InputVertices</a> <font color="Maroon" title="c7">S</font>
 ;<br/>

<a NAME="E4:83"/>
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c7">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="msafree2.html#K2" title="MSAFREE2:func.2">InputVertices</a> <font color="Maroon" title="c7">S</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="msafree2.html#K4" title="MSAFREE2:func.4">InnerVertices</a> <font color="Maroon" title="c7">S</font></span>)</span>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T45" title="XBOOLE_1:th.45">XBOOLE_1:45</a></i>;<br/>
<a NAME="E5:83"/><b>then </b><i><font color="Green" title="E42">A4</font></i>: 
<font color="Maroon" title="c1">x1</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1">(<span class="default"><a href="msafree2.html#K4" title="MSAFREE2:func.4">InnerVertices</a> <font color="Maroon" title="c7">S</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="msafree2.html#K2" title="MSAFREE2:func.2">InputVertices</a> <font color="Maroon" title="c7">S</font>
 
<b>by </b><i><a class="txt" href="circcmb3.html#E2:83"><i><font color="Green" title="E40">A2</font></i></a>, <a class="ref" href="xboole_1.html#T43" title="XBOOLE_1:th.43">XBOOLE_1:43</a></i>;<br/>
<a NAME="E6:83"/>
<font color="Maroon" title="c7">S</font> <a href="circcomb.html#R1" title="CIRCCOMB:pred.1">tolerates</a>  <a href="circcmb3.html#K6" title="CIRCCMB3:func.6">1GateCircStr</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c5">f</font>
 
<b>by </b><i><a class="ref" href="circcomb.html#T55" title="CIRCCOMB:th.55">CIRCCOMB:55</a></i>;<br/>
<b>hence </b> <a href="msafree2.html#K2" title="MSAFREE2:func.2">InputVertices</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">S</font> <a href="circcmb3.html#K8" title="CIRCCMB3:func.8">+*</a> <span class="p2">(<span class="default"><a href="circcmb3.html#K6" title="CIRCCMB3:func.6">1GateCircStr</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c5">f</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msafree2.html#K2" title="MSAFREE2:func.2">InputVertices</a> <font color="Maroon" title="c7">S</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2">(<span class="default"><a href="msafree2.html#K4" title="MSAFREE2:func.4">InnerVertices</a> <span class="p3">(<span class="default"><a href="circcmb3.html#K6" title="CIRCCMB3:func.6">1GateCircStr</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c5">f</font></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msafree2.html#K2" title="MSAFREE2:func.2">InputVertices</a> <span class="p3">(<span class="default"><a href="circcmb3.html#K6" title="CIRCCMB3:func.6">1GateCircStr</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c5">f</font></span>)</span></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2">(<span class="default"><a href="msafree2.html#K4" title="MSAFREE2:func.4">InnerVertices</a> <font color="Maroon" title="c7">S</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="circcmb2.html#T6" title="CIRCCMB2:th.6">CIRCCMB2:6</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msafree2.html#K2" title="MSAFREE2:func.2">InputVertices</a> <font color="Maroon" title="c7">S</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2">(<span class="default"><a href="msafree2.html#K4" title="MSAFREE2:func.4">InnerVertices</a> <span class="p3">(<span class="default"><a href="circcmb3.html#K6" title="CIRCCMB3:func.6">1GateCircStr</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c5">f</font></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c6">p</font></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p2">(<span class="default"><a href="msafree2.html#K4" title="MSAFREE2:func.4">InnerVertices</a> <font color="Maroon" title="c7">S</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="circcomb.html#T49" title="CIRCCOMB:th.49">CIRCCOMB:49</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msafree2.html#K2" title="MSAFREE2:func.2">InputVertices</a> <font color="Maroon" title="c7">S</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2">(<span class="default"><a href="msafree2.html#K4" title="MSAFREE2:func.4">InnerVertices</a> <span class="p3">(<span class="default"><a href="circcmb3.html#K6" title="CIRCCMB3:func.6">1GateCircStr</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c5">f</font></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">x1</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p3">(<span class="default"><a href="msafree2.html#K4" title="MSAFREE2:func.4">InnerVertices</a> <font color="Maroon" title="c7">S</font></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">x2</font></span>)</span>
<b>by </b><i><a class="txt" href="circcmb3.html#E1:83"><i><font color="Green" title="E39">A1</font></i></a>, <a class="txt" href="circcmb3.html#E2:83"><i><font color="Green" title="E40">A2</font></i></a>, <a class="ref" href="xboole_1.html#T87" title="XBOOLE_1:th.87">XBOOLE_1:87</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="msafree2.html#K2" title="MSAFREE2:func.2">InputVertices</a> <font color="Maroon" title="c7">S</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3">(<span class="default"><a href="msafree2.html#K4" title="MSAFREE2:func.4">InnerVertices</a> <span class="p4">(<span class="default"><a href="circcmb3.html#K6" title="CIRCCMB3:func.6">1GateCircStr</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c5">f</font></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">x1</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p3">(<span class="default"><a href="msafree2.html#K4" title="MSAFREE2:func.4">InnerVertices</a> <font color="Maroon" title="c7">S</font></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">x2</font>
<b>by </b><i><a class="ref" href="xboole_1.html#T4" title="XBOOLE_1:th.4">XBOOLE_1:4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="msafree2.html#K2" title="MSAFREE2:func.2">InputVertices</a> <font color="Maroon" title="c7">S</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p4">(<span class="default"><a href="circcmb3.html#K5" title="CIRCCMB3:func.5">Output</a> <span class="p5">(<span class="default"><a href="circcmb3.html#K6" title="CIRCCMB3:func.6">1GateCircStr</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c5">f</font></span>)</span></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">x1</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p3">(<span class="default"><a href="msafree2.html#K4" title="MSAFREE2:func.4">InnerVertices</a> <font color="Maroon" title="c7">S</font></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">x2</font>
<b>by </b><i><a class="ref" href="circcmb3.html#T17" target="_self" title="CIRCCMB3:th.17">Th17</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msafree2.html#K2" title="MSAFREE2:func.2">InputVertices</a> <font color="Maroon" title="c7">S</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">x1</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p3">(<span class="default"><a href="msafree2.html#K4" title="MSAFREE2:func.4">InnerVertices</a> <font color="Maroon" title="c7">S</font></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">x2</font>
<b>by </b><i><a class="txt" href="circcmb3.html#E3:83"><i><font color="Green" title="E41">A3</font></i></a>, <a class="ref" href="zfmisc_1.html#T65" title="ZFMISC_1:th.65">ZFMISC_1:65</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="msafree2.html#K2" title="MSAFREE2:func.2">InputVertices</a> <font color="Maroon" title="c7">S</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">x2</font>
<b>by </b><i><a class="txt" href="circcmb3.html#E5:83"><i><font color="Green" title="E42">A4</font></i></a>, <a class="ref" href="xboole_1.html#T12" title="XBOOLE_1:th.12">XBOOLE_1:12</a></i>
;<br/><br/>


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