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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="E1:15"/>
<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="E2:15"/><b>then </b><i><font color="Green">E6</font></i>: 
the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">c<sub>1</sub></font> <a href="partfun1.html#R1">tolerates</a> the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="circcomb.html#D1">CIRCCOMB:def 1</a></i>;<br/>
<i><font color="Green">E7</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> = 
the <a href="struct_0.html#U1">carrier</a> of <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="xboole_0.html#K4">\</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">c<sub>1</sub></font> <a href="circcomb.html#K3">+*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>

<br/>.= 
the <a href="struct_0.html#U1">carrier</a> of <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="xboole_0.html#K4">\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p2">(<span class="default">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></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="circcomb.html#D2">CIRCCOMB:def 2</a></i>
<br/>.= 
<span class="p1">(<span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#K2">\/</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xboole_0.html#K4">\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p2">(<span class="default">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></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="circcomb.html#D2">CIRCCOMB:def 2</a></i>
<br/>.= 
<span class="p1">(<span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#K2">\/</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xboole_0.html#K4">\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2">(<span class="default"><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></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="circcmb2.html#E2:15"><i><font color="Green">E6</font></i></a>, <a class="ref" href="circcmb2.html#T5" target="_self">Th5</a></i>
<br/>.= 
<span class="p1">(<span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#K4">\</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="relat_1.html#K2">rng</a> the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p3">(<span class="default"><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></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> <a href="xboole_0.html#K4">\</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="relat_1.html#K2">rng</a> the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p3">(<span class="default"><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></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T42">XBOOLE_1:42</a></i>
;<br/>
<i><font color="Green">E8</font></i>: the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#K4">\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2">(<span class="default"><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></span>)</span></span>)</span> = 
<span class="p1">(<span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#K4">\</a> <span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="xboole_0.html#K4">\</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">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T41">XBOOLE_1:41</a></i>
<br/>.= 
<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#K4">\</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">c<sub>2</sub></font></span>)</span>

<br/>.= 
<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#K4">\</a> <span class="p1">(<span class="default"><a href="msafree2.html#K3">InnerVertices</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>

;<br/>
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> <a href="xboole_0.html#K4">\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2">(<span class="default"><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></span>)</span></span>)</span> = 
<span class="p1">(<span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> <a href="xboole_0.html#K4">\</a> <span class="p2">(<span class="default"><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></span>)</span></span>)</span> <a href="xboole_0.html#K4">\</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">c<sub>1</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T41">XBOOLE_1:41</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="msafree2.html#K2">InputVertices</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xboole_0.html#K4">\</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">c<sub>1</sub></font></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><a href="msafree2.html#K2">InputVertices</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xboole_0.html#K4">\</a> <span class="p1">(<span class="default"><a href="msafree2.html#K3">InnerVertices</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>

;<br/>
<b>hence </b><a NAME="E6:15"/>
 <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="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<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#K4">\</a> <span class="p2">(<span class="default"><a href="msafree2.html#K3">InnerVertices</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msafree2.html#K2">InputVertices</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xboole_0.html#K4">\</a> <span class="p2">(<span class="default"><a href="msafree2.html#K3">InnerVertices</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="circcmb2.html#E3:15"><i><font color="Green">E7</font></i></a>, <a class="txt" href="circcmb2.html#E4:15"><i><font color="Green">E8</font></i></a></i>;<br/>


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