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<b>let </b><font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>6</sub></font> be   <a href="triang_1.html#NM4">Symplex</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:44_1_2"/><i><font color="Green">E14</font></i>: 
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="funct_1.html#NM1">Function</a> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> the <a href="triang_1.html#U2" target="_self">FacesAssign</a> of <font color="Maroon">c<sub>1</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font> holds <br/><font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>3</sub></font>
 <b>and </b><br/><a NAME="E2:44_1_2"/><i><font color="Green">E15</font></i>: 
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="funct_1.html#NM1">Function</a> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> the <a href="triang_1.html#U2" target="_self">FacesAssign</a> of <font color="Maroon">c<sub>1</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font> holds <br/><font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<b>reconsider </b><font color="Maroon">c<sub>7</sub></font> = the <a href="triang_1.html#U2" target="_self">FacesAssign</a> of <font color="Maroon">c<sub>1</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>2</sub></font> as   <a href="funct_2.html#NM1">Function</a> of <a href="triang_1.html#K6" target="_self">NatEmbSeq</a>  <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p1">(<span class="default"><a href="triang_1.html#K4" target="_self">FuncsSeq</a> the <a href="triang_1.html#U1" target="_self">SkeletonSeq</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>2</sub></font> <b>by </b><i><a class="ref" href="pboole.html#D18">PBOOLE:def 18</a></i>;<br/>
<a NAME="E4:44_1_2"/>
<font color="Maroon">c<sub>7</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="triang_1.html#K4" target="_self">FuncsSeq</a> the <a href="triang_1.html#U1" target="_self">SkeletonSeq</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>2</sub></font>
 
;<br/>
<a NAME="E5:44_1_2"/><b>then </b>
<font color="Maroon">c<sub>7</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="funct_2.html#K1">Funcs</a> <span class="p1">(<span class="default">the <a href="triang_1.html#U1" target="_self">SkeletonSeq</a> of <font color="Maroon">c<sub>1</sub></font> <a href="funct_1.html#K1">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default">the <a href="triang_1.html#U1" target="_self">SkeletonSeq</a> of <font color="Maroon">c<sub>1</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="triang_1.html#D5" target="_self">Def5</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>8</sub></font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E7:44_1_2"/><i><font color="Green">E16</font></i>: 
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>4</sub></font>
 <b>and </b><br/><a NAME="E8:44_1_2"/>
(  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> the <a href="triang_1.html#U1" target="_self">SkeletonSeq</a> of <font color="Maroon">c<sub>1</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> &amp;  <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>8</sub></font> <a href="tarski.html#R1">c=</a> the <a href="triang_1.html#U1" target="_self">SkeletonSeq</a> of <font color="Maroon">c<sub>1</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>2</sub></font> )
 <b>by </b><i><a class="ref" href="funct_2.html#D2">FUNCT_2:def 2</a></i>;<br/>
<a NAME="E9:44_1_2"/>
( <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>3</sub></font> )
 
<b>by </b><i><a class="txt" href="triang_1.html#E1:44_1_2"><i><font color="Green">E14</font></i></a>, <a class="txt" href="triang_1.html#E2:44_1_2"><i><font color="Green">E15</font></i></a>, <a class="txt" href="triang_1.html#E7:44_1_2"><i><font color="Green">E16</font></i></a></i>;<br/>
<b>hence </b><a NAME="E10:44_1_2"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font>
 ;<br/>


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