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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="msualg_1.html#L1">ManySortedSign</a> ;<br/>

<b>assume </b><a NAME="E1:26"/>
<font color="Maroon">c<sub>1</sub></font> <a href="circcomb.html#R1">tolerates</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<a NAME="E2:26"/><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="tarski.html#R1">c=</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="ref" href="circcomb.html#T15">CIRCCOMB:15</a></i>;<br/>
<b>assume </b><a NAME="E3:26"/><i><font color="Green">E12</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being <a href="facirc_1.html#V1" target="_self">pair</a>  <a href="hidden.html#M1">set</a>  holds not <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="msafree2.html#K2">InputVertices</a> <font color="Maroon">c<sub>1</sub></font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="facirc_1.html#D2" target="_self">FACIRC_1:def 2</a><br/>

<b>assume </b><a NAME="E4:26"/><i><font color="Green">E13</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being <a href="facirc_1.html#V1" target="_self">pair</a>  <a href="hidden.html#M1">set</a>  holds not <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="msafree2.html#K2">InputVertices</a> <font color="Maroon">c<sub>2</sub></font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="facirc_1.html#D2" target="_self">FACIRC_1:def 2</a><br/>

<b>let </b><font color="Maroon">c<sub>3</sub></font> be  <a href="facirc_1.html#V1" target="_self">pair</a>  <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="facirc_1.html#D2" target="_self">FACIRC_1:def 2</a><br/>

<b>assume </b><a NAME="E5:26"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <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>
 ;<br/>

<a NAME="E6:26"/><b>then </b>
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="msafree2.html#K2">InputVertices</a> <font color="Maroon">c<sub>1</sub></font> or <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</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#E2:26"><i><font color="Green">E11</font></i></a>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>
<b>hence </b><a NAME="E7:26"/>
contradiction
 <b>by </b><i><a class="txt" href="facirc_1.html#E3:26"><i><font color="Green">E12</font></i></a>, <a class="txt" href="facirc_1.html#E4:26"><i><font color="Green">E13</font></i></a></i>;<br/>


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