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<b>let </b><font color="Maroon">S</font> be  non <a href="struct_0.html#V3">empty</a> <a href="circcmb3.html#V6" target="_self">with_nonpair_inputs</a>  <a href="msualg_1.html#L1">ManySortedSign</a> ;<br/><b>let </b><font color="Maroon">x</font> be   <a href="msafree2.html#NM1">Vertex</a> of <font color="Maroon">S</font>;<br/>



<a NAME="E1:110"/>
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="msafree2.html#K2">InputVertices</a> <font color="Maroon">S</font></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><a href="msafree2.html#K3">InnerVertices</a> <font color="Maroon">S</font></span>)</span>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T45">XBOOLE_1:45</a></i>;<br/>
<a NAME="E2:110"/><b>then </b>
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="msafree2.html#K2">InputVertices</a> <font color="Maroon">S</font> or <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="msafree2.html#K3">InnerVertices</a> <font color="Maroon">S</font> )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>
<b>hence </b><a NAME="E3:110"/>
( <font color="Maroon">x</font> is <a href="facirc_1.html#V1">pair</a> implies <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="msafree2.html#K3">InnerVertices</a> <font color="Maroon">S</font> )
 <b>by </b><i><a class="ref" href="facirc_1.html#D2">FACIRC_1:def 2</a></i>;<br/>


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