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<b>let </b><font color="Maroon" title="c1">S1</font>, <font color="Maroon" title="c2">S</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> non <a href="msualg_1.html#V2" title="MSUALG_1:attr.2">void</a> <a href="msafree2.html#V2" title="MSAFREE2:attr.2">Circuit-like</a>  <a href="msualg_1.html#L1" title="MSUALG_1:struct.1">ManySortedSign</a> ;<br/><b>let </b><font color="Maroon" title="c3">S2</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a>  <a href="msualg_1.html#L1" title="MSUALG_1:struct.1">ManySortedSign</a> ;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:31"/><i><font color="Green" title="E20">A1</font></i>: 
<font color="Maroon" title="c1">S1</font> <a href="circcomb.html#R1" title="CIRCCOMB:pred.1">tolerates</a> <font color="Maroon" title="c3">S2</font>
 <b>and </b><br/><a NAME="E2:31"/><i><font color="Green" title="E21">A2</font></i>: 
<font color="Maroon" title="c2">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">S1</font> <a href="circcomb.html#K3" title="CIRCCOMB:func.3">+*</a> <font color="Maroon" title="c3">S2</font>
 ;<br/>

<b>let </b><font color="Maroon" title="c4">v1</font> be   <a href="msafree2.html#NM1" title="MSAFREE2:NM.1">Vertex</a> of <font color="Maroon" title="c1">S1</font>;<br/>

<b>assume </b><a NAME="E3:31"/><i><font color="Green" title="E22">A3</font></i>: 
<font color="Maroon" title="c4">v1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="msafree2.html#K4" title="MSAFREE2:func.4">InnerVertices</a> <font color="Maroon" title="c1">S1</font>
 ;<br/>

<b>let </b><font color="Maroon" title="c5">v</font> be   <a href="msafree2.html#NM1" title="MSAFREE2:NM.1">Vertex</a> of <font color="Maroon" title="c2">S</font>;<br/>

<b>assume </b><a NAME="E4:31"/><i><font color="Green" title="E23">A4</font></i>: 
<font color="Maroon" title="c4">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">v</font>
 ;<br/>

<a NAME="E5:31"/>
 <a href="msafree2.html#K4" title="MSAFREE2:func.4">InnerVertices</a> <font color="Maroon" title="c2">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="msafree2.html#K4" title="MSAFREE2:func.4">InnerVertices</a> <font color="Maroon" title="c1">S1</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="msafree2.html#K3" title="MSAFREE2:func.3">InnerVertices</a> <font color="Maroon" title="c3">S2</font></span>)</span>
 
<b>by </b><i><a class="txt" href="circcomb.html#E1:31"><i><font color="Green" title="E20">A1</font></i></a>, <a class="txt" href="circcomb.html#E2:31"><i><font color="Green" title="E21">A2</font></i></a>, <a class="ref" href="circcomb.html#T15" target="_self" title="CIRCCOMB:th.15">Th15</a></i>;<br/>
<b>hence </b><a NAME="E6:31"/><i><font color="Green" title="E24">A5</font></i>: 
<font color="Maroon" title="c5">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="msafree2.html#K4" title="MSAFREE2:func.4">InnerVertices</a> <font color="Maroon" title="c2">S</font>
 <b>by </b><i><a class="txt" href="circcomb.html#E3:31"><i><font color="Green" title="E22">A3</font></i></a>, <a class="txt" href="circcomb.html#E4:31"><i><font color="Green" title="E23">A4</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/>

<a NAME="E7:31"/><b>then </b><i><font color="Green" title="E25">A6</font></i>: 
(  <a href="msualg_1.html#K2" title="MSUALG_1:func.2">the_result_sort_of</a> <span class="p1">(<span class="default"><a href="msafree2.html#K5" title="MSAFREE2:func.5">action_at</a> <font color="Maroon" title="c4">v1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">v1</font> &amp;  <a href="msualg_1.html#K2" title="MSUALG_1:func.2">the_result_sort_of</a> <span class="p1">(<span class="default"><a href="msafree2.html#K5" title="MSAFREE2:func.5">action_at</a> <font color="Maroon" title="c5">v</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">v</font> )
 
<b>by </b><i><a class="txt" href="circcomb.html#E3:31"><i><font color="Green" title="E22">A3</font></i></a>, <a class="ref" href="msafree2.html#D7" title="MSAFREE2:def.7">MSAFREE2:def 7</a></i>;<br/>
<a NAME="E8:31"/>
( the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">OperSymbols</a> of <font color="Maroon" title="c2">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">OperSymbols</a> of <font color="Maroon" title="c1">S1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">OperSymbols</a> of <font color="Maroon" title="c3">S2</font> &amp;  <a href="msafree2.html#K5" title="MSAFREE2:func.5">action_at</a> <font color="Maroon" title="c4">v1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">OperSymbols</a> of <font color="Maroon" title="c1">S1</font> )
 
<b>by </b><i><a class="txt" href="circcomb.html#E2:31"><i><font color="Green" title="E21">A2</font></i></a>, <a class="ref" href="circcomb.html#D2" target="_self" title="CIRCCOMB:def.2">Def2</a>, <a class="txt" href="circcomb.html#E2"><i><font color="Green" title="E2">Lm2</font></i></a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c6">o</font> =  <a href="msafree2.html#K5" title="MSAFREE2:func.5">action_at</a> <font color="Maroon" title="c4">v1</font> as   <a href="msualg_1.html#NM2" title="MSUALG_1:NM.2">OperSymbol</a> of <font color="Maroon" title="c2">S</font> <b>by </b><i><a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/>
<a NAME="E10:31"/>
<font color="Maroon" title="c5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="msualg_1.html#K2" title="MSUALG_1:func.2">the_result_sort_of</a> <font color="Maroon" title="c6">o</font>
 
<b>by </b><i><a class="txt" href="circcomb.html#E1:31"><i><font color="Green" title="E20">A1</font></i></a>, <a class="txt" href="circcomb.html#E2:31"><i><font color="Green" title="E21">A2</font></i></a>, <a class="txt" href="circcomb.html#E4:31"><i><font color="Green" title="E23">A4</font></i></a>, <a class="txt" href="circcomb.html#E7:31"><i><font color="Green" title="E25">A6</font></i></a>, <a class="ref" href="circcomb.html#T20" target="_self" title="CIRCCOMB:th.20">Th20</a></i>;<br/>
<b>hence </b><a NAME="E11:31"/>
 <a href="msafree2.html#K5" title="MSAFREE2:func.5">action_at</a> <font color="Maroon" title="c5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="msafree2.html#K5" title="MSAFREE2:func.5">action_at</a> <font color="Maroon" title="c4">v1</font>
 <b>by </b><i><a class="txt" href="circcomb.html#E6:31"><i><font color="Green" title="E24">A5</font></i></a>, <a class="ref" href="msafree2.html#D7" title="MSAFREE2:def.7">MSAFREE2:def 7</a></i>;<br/>


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