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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="struct_0.html#V3">empty</a>  <a href="msualg_1.html#L1">ManySortedSign</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be  non <a href="struct_0.html#V3">empty</a> non <a href="msualg_1.html#V2">void</a> <a href="msafree2.html#V2">Circuit-like</a>  <a href="msualg_1.html#L1">ManySortedSign</a> ;<br/>



<b>assume </b><a NAME="E1:29"/><i><font color="Green">E18</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="circcomb.html#K3" target="_self">+*</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="msafree2.html#NM1">Vertex</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>

<b>assume </b><a NAME="E2:29"/><i><font color="Green">E19</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="msafree2.html#K4">InnerVertices</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<b>let </b><font color="Maroon">c<sub>5</sub></font> be   <a href="msafree2.html#NM1">Vertex</a> of <font color="Maroon">c<sub>3</sub></font>;<br/>

<b>assume </b><a NAME="E3:29"/><i><font color="Green">E20</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font>
 ;<br/>

<a NAME="E4:29"/>
( the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">c<sub>1</sub></font> <a href="funct_4.html#K1">+*</a> the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">c<sub>2</sub></font> &amp;  <a href="msafree2.html#K4">InnerVertices</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K2">rng</a> the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">c<sub>2</sub></font> &amp;  <a href="msafree2.html#K4">InnerVertices</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K2">rng</a> the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">c<sub>3</sub></font> )
 
<b>by </b><i><a class="txt" href="circcomb.html#E1:29"><i><font color="Green">E18</font></i></a>, <a class="ref" href="circcomb.html#D2" target="_self">Def2</a></i>;<br/>
<a NAME="E5:29"/><b>then </b><i><font color="Green">E21</font></i>: 
 <a href="msafree2.html#K4">InnerVertices</a> <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a>  <a href="msafree2.html#K4">InnerVertices</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="funct_4.html#T19">FUNCT_4:19</a></i>;<br/>
<b>hence </b><a NAME="E6:29"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="msafree2.html#K4">InnerVertices</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="circcomb.html#E2:29"><i><font color="Green">E19</font></i></a>, <a class="txt" href="circcomb.html#E3:29"><i><font color="Green">E20</font></i></a></i>;<br/>

<a NAME="E7:29"/><i><font color="Green">E22</font></i>: 
(  <a href="msualg_1.html#K2">the_result_sort_of</a> <span class="p1">(<span class="default"><a href="msafree2.html#K5">action_at</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> &amp;  <a href="msualg_1.html#K2">the_result_sort_of</a> <span class="p1">(<span class="default"><a href="msafree2.html#K5">action_at</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> )
 
<b>by </b><i><a class="txt" href="circcomb.html#E2:29"><i><font color="Green">E19</font></i></a>, <a class="txt" href="circcomb.html#E3:29"><i><font color="Green">E20</font></i></a>, <a class="txt" href="circcomb.html#E5:29"><i><font color="Green">E21</font></i></a>, <a class="ref" href="msafree2.html#D7">MSAFREE2:def 7</a></i>;<br/>
<a NAME="E8:29"/>
( the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#K2">\/</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">c<sub>2</sub></font> &amp;  <a href="msafree2.html#K5">action_at</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="txt" href="circcomb.html#E1:29"><i><font color="Green">E18</font></i></a>, <a class="ref" href="circcomb.html#D2" target="_self">Def2</a>, <a class="txt" href="circcomb.html#E2"><i><font color="Green">Lemma2</font></i></a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>6</sub></font> =  <a href="msafree2.html#K5">action_at</a> <font color="Maroon">c<sub>4</sub></font> as   <a href="msualg_1.html#NM2">OperSymbol</a> of <font color="Maroon">c<sub>3</sub></font> <b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>
<a NAME="E10:29"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="msualg_1.html#K2">the_result_sort_of</a> <font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="txt" href="circcomb.html#E1:29"><i><font color="Green">E18</font></i></a>, <a class="txt" href="circcomb.html#E3:29"><i><font color="Green">E20</font></i></a>, <a class="txt" href="circcomb.html#E7:29"><i><font color="Green">E22</font></i></a>, <a class="ref" href="circcomb.html#T18" target="_self">Th18</a></i>;<br/>
<b>hence </b><a NAME="E11:29"/>
 <a href="msafree2.html#K5">action_at</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="msafree2.html#K5">action_at</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="circcomb.html#E2:29"><i><font color="Green">E19</font></i></a>, <a class="txt" href="circcomb.html#E3:29"><i><font color="Green">E20</font></i></a>, <a class="txt" href="circcomb.html#E5:29"><i><font color="Green">E21</font></i></a>, <a class="ref" href="msafree2.html#D7">MSAFREE2:def 7</a></i>;<br/>


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