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<b>let </b><font color="Maroon">S1</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="msualg_1.html#L1">ManySortedSign</a> , <font color="Maroon">S2</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="E1:27"/><i><font color="Green">E24</font></i>: 
( the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">S1</font> <a href="partfun1.html#R1">tolerates</a> the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">S2</font> &amp; the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">S1</font> <a href="partfun1.html#R1">tolerates</a> the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">S2</font> )
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="circcomb.html#D1" target="_self">CIRCCOMB:def 1</a><br/>

<b>set </b><font color="Maroon">R1</font> = the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">S1</font>;<br/>
<b>set </b><font color="Maroon">R2</font> = the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">S2</font>;<br/>
<b>set </b><font color="Maroon">S</font> = <font color="Maroon">S1</font> <a href="circcomb.html#K3" target="_self">+*</a> <font color="Maroon">S2</font>;<br/>
<b>set </b><font color="Maroon">R</font> = the <a href="msualg_1.html#U3">ResultSort</a> of <span class="p1">(<span class="default"><font color="Maroon">S1</font> <a href="circcomb.html#K3" target="_self">+*</a> <font color="Maroon">S2</font></span>)</span>;<br/>
<a NAME="E2:27"/>
the <a href="msualg_1.html#U3">ResultSort</a> of <span class="p1">(<span class="default"><font color="Maroon">S1</font> <a href="circcomb.html#K3" target="_self">+*</a> <font color="Maroon">S2</font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">S1</font> <a href="funct_4.html#K1">+*</a> the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">S2</font>
 
<b>by </b><i/>;<br/>
<a NAME="E3:27"/><b>then </b>
the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">S1</font> <a href="tarski.html#R1">c=</a> the <a href="msualg_1.html#U3">ResultSort</a> of <span class="p1">(<span class="default"><font color="Maroon">S1</font> <a href="circcomb.html#K3" target="_self">+*</a> <font color="Maroon">S2</font></span>)</span>
 
<b>by </b><i>, <a class="ref" href="funct_4.html#T29">FUNCT_4:29</a></i>;<br/>
<a NAME="E4:27"/><b>then </b><i><font color="Green">E33</font></i>: 
 <a href="relat_1.html#K2">rng</a> the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">S1</font> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K2">rng</a> the <a href="msualg_1.html#U3">ResultSort</a> of <span class="p1">(<span class="default"><font color="Maroon">S1</font> <a href="circcomb.html#K3" target="_self">+*</a> <font color="Maroon">S2</font></span>)</span>
 
<b>by </b><i><a class="ref" href="relat_1.html#T25">RELAT_1:25</a></i>;<br/>
<b>let </b><font color="Maroon">v1</font> be   <a href="msafree2.html#NM1">Vertex</a> of <font color="Maroon">S1</font>;<br/>

<b>assume </b><a NAME="E5:27"/>
<font color="Maroon">v1</font> <a href="hidden.html#R2">in</a>  <a href="msafree2.html#K2">InputVertices</a> <span class="p1">(<span class="default"><font color="Maroon">S1</font> <a href="circcomb.html#K3" target="_self">+*</a> <font color="Maroon">S2</font></span>)</span>
 ;<br/>

<a NAME="E6:27"/><b>then </b>
<font color="Maroon">v1</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon">S1</font> <a href="circcomb.html#K3" target="_self">+*</a> <font color="Maroon">S2</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> the <a href="msualg_1.html#U3">ResultSort</a> of <span class="p2">(<span class="default"><font color="Maroon">S1</font> <a href="circcomb.html#K3" target="_self">+*</a> <font color="Maroon">S2</font></span>)</span></span>)</span>
 
;<br/>
<a NAME="E7:27"/><b>then </b>
not <font color="Maroon">v1</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">S1</font>
 
<b>by </b><i>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/>
<a NAME="E8:27"/><b>then </b>
<font color="Maroon">v1</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S1</font> <a href="subset_1.html#K6">\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">S1</font></span>)</span>
 
<b>by </b><i><a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/>
<b>hence </b><a NAME="E9:27"/>
<font color="Maroon">v1</font> <a href="hidden.html#R2">in</a>  <a href="msafree2.html#K2">InputVertices</a> <font color="Maroon">S1</font>
 ;<br/>


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