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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> non <a href="msualg_1.html#V2">void</a>  <a href="msualg_1.html#L1">ManySortedSign</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be  <a href="relat_1.html#V2">V5</a>  <a href="pboole.html#M1">ManySortedSet</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be  non <a href="xboole_0.html#V1">empty</a> <a href="subset_1.html#NM2">Subset</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="msaterm.html#K1">-Terms</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="msafree2.html#NM1">Vertex</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="circtrm1.html#K1" target="_self">-CircuitStr</a> </span>)</span>;<br/>







<b>thus </b><a NAME="E1:8"/>
( <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 <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="circtrm1.html#K1" target="_self">-CircuitStr</a> </span>)</span> implies <font color="Maroon">c<sub>4</sub></font> is    <a href="msaterm.html#M2">CompoundTerm</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> )
 <b>by </b><i><a class="ref" href="circtrm1.html#T4" target="_self">Th4</a></i>;<br/>

<b>set </b><font color="Maroon">c<sub>5</sub></font> = <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">c<sub>1</sub></font>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K1">}</a></span></span><a href="zfmisc_1.html#K2">:]</a></span>;<br/>
<b>consider </b><font color="Maroon">c<sub>6</sub></font> being    <a href="trees_3.html#M3">Element</a> of <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>7</sub></font> being   <a href="trees_4.html#NM1">Node</a> of <font color="Maroon">c<sub>6</sub></font><b> such that </b><br/><a NAME="E3:8"/><i><font color="Green">E6</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> <a href="trees_2.html#K5">|</a> <font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="ref" href="trees_9.html#T20">TREES_9:20</a></i>;<br/>
<b>assume </b><a NAME="E4:8"/>
<font color="Maroon">c<sub>4</sub></font> is    <a href="msaterm.html#M2">CompoundTerm</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<b>then reconsider </b><font color="Maroon">c<sub>8</sub></font> = <font color="Maroon">c<sub>4</sub></font> as    <a href="msaterm.html#M2">CompoundTerm</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> ;<br/>
<a NAME="E6:8"/>
( <font color="Maroon">c<sub>8</sub></font> <a href="funct_1.html#K1">.</a> <a href="xboole_0.html#K1">{}</a>  <a href="hidden.html#R2">in</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">c<sub>1</sub></font>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K1">}</a></span></span><a href="zfmisc_1.html#K2">:]</a></span> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="finseq_1.html#K8">^</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K6">&lt;*&gt;</a> <a href="numbers.html#K5">NAT</a> </span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> &amp;  <a href="xboole_0.html#K1">{}</a>  <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="trees_1.html#K4">|</a> <font color="Maroon">c<sub>7</sub></font> )
 
<b>by </b><i><a class="ref" href="finseq_1.html#T47">FINSEQ_1:47</a>, <a class="ref" href="msaterm.html#D6">MSATERM:def 6</a>, <a class="ref" href="trees_1.html#T47">TREES_1:47</a></i>;<br/>
<a NAME="E7:8"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">c<sub>1</sub></font>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K1">}</a></span></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i><a class="txt" href="circtrm1.html#E3:8"><i><font color="Green">E6</font></i></a>, <a class="ref" href="trees_2.html#D11">TREES_2:def 11</a></i>;<br/>
<b>hence </b><a NAME="E8:8"/>
<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 <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="circtrm1.html#K1" target="_self">-CircuitStr</a> </span>)</span>
 <b>by </b><i><a class="txt" href="circtrm1.html#E3:8"><i><font color="Green">E6</font></i></a>, <a class="ref" href="trees_9.html#T25">TREES_9:25</a></i>;<br/>


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