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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be  non <a href="struct_0.html#V3">empty</a> <a href="circcomb.html#V1">unsplit</a> <a href="circcomb.html#V2">gate`1=arity</a>  <a href="msualg_1.html#L1">ManySortedSign</a> ;<br/>

<b>assume </b><a NAME="E1:25"/><i><font color="Green">E10</font></i>: 
( not  <a href="msafree2.html#K2">InputVertices</a> <font color="Maroon">c<sub>1</sub></font> is <a href="facirc_1.html#V2" target="_self">with_pair</a> &amp;  <a href="msafree2.html#K3">InnerVertices</a> <font color="Maroon">c<sub>1</sub></font> is   <a href="relat_1.html#NM1">Relation</a> &amp; not  <a href="msafree2.html#K2">InputVertices</a> <font color="Maroon">c<sub>2</sub></font> is <a href="facirc_1.html#V2" target="_self">with_pair</a> &amp;  <a href="msafree2.html#K3">InnerVertices</a> <font color="Maroon">c<sub>2</sub></font> is   <a href="relat_1.html#NM1">Relation</a> )
 ;<br/>

<a NAME="E2:25"/><b>then </b><i><font color="Green">E11</font></i>: 
 <a href="msafree2.html#K2">InputVertices</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="circcomb.html#K3">+*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="msafree2.html#K2">InputVertices</a> <font color="Maroon">c<sub>1</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="msafree2.html#K2">InputVertices</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2">(<span class="default"><a href="msafree2.html#K3">InnerVertices</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="facirc_1.html#T6" target="_self">Th6</a></i>;<br/>
<a NAME="E3:25"/>
 <a href="msafree2.html#K3">InnerVertices</a> <font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#R1">misses</a>  <a href="msafree2.html#K2">InputVertices</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="facirc_1.html#E1:25"><i><font color="Green">E10</font></i></a>, <a class="ref" href="facirc_1.html#T5" target="_self">Th5</a></i>;<br/>
<b>hence </b><a NAME="E4:25"/>
 <a href="msafree2.html#K2">InputVertices</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="circcomb.html#K3">+*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="msafree2.html#K2">InputVertices</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="msafree2.html#K2">InputVertices</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="facirc_1.html#E2:25"><i><font color="Green">E11</font></i></a>, <a class="ref" href="xboole_1.html#T83">XBOOLE_1:83</a></i>;<br/>


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