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<b>let </b><font color="Maroon">S</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">V</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">S</font>;<br/><b>let </b><font color="Maroon">X</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">S</font> <a href="msaterm.html#K1">-Terms</a> <font color="Maroon">V</font></span>)</span>;<br/>





<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:5_1"/>
<font color="Maroon">X</font> is    <a href="msaterm.html#M3">SetWithCompoundTerm</a> of <font color="Maroon">S</font>,<font color="Maroon">V</font>
 ;<br/><b>then consider </b><font color="Maroon">t</font> being    <a href="msaterm.html#M2">CompoundTerm</a> of <font color="Maroon">S</font>,<font color="Maroon">V</font><b> such that </b><br/><a NAME="E3:5_1"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">t</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font>
 <b>by </b><i><a class="ref" href="msaterm.html#D7">MSATERM:def 7</a></i>;<br/><a NAME="E4:5_1"/>
<font color="Maroon">t</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">S</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">S</font></span><a href="tarski.html#K1">}</a></span></span><a href="zfmisc_1.html#K2">:]</a></span>
 <b>by </b><i><a class="ref" href="msaterm.html#D6">MSATERM:def 6</a></i>;<br/><b>hence </b><a NAME="E5:5_1"/>
not <font color="Maroon">X</font> <a href="circtrm1.html#K1" target="_self">-CircuitStr</a>  is <a href="msualg_1.html#V2">void</a>
 <b>by </b><i>, </i>;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E2:5"/>
not <font color="Maroon">X</font> <a href="circtrm1.html#K1" target="_self">-CircuitStr</a>  is <a href="msualg_1.html#V2">void</a>
 ;<br/>

<b>then consider </b><font color="Maroon">t</font> being    <a href="trees_3.html#M3">Element</a> of <font color="Maroon">X</font><b> such that </b><br/><a NAME="E4:5"/><i><font color="Green">E39</font></i>: 
(  not <font color="Maroon">t</font> is <a href="trees_9.html#V1">root</a> or <font color="Maroon">t</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">S</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">S</font></span><a href="tarski.html#K1">}</a></span></span><a href="zfmisc_1.html#K2">:]</a></span> )
 <b>by </b><i/>;<br/>
<a NAME="E5:5"/>
<font color="Maroon">t</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font>
 
;<br/>
<a NAME="E6:5"/><b>then </b>
<font color="Maroon">t</font> is    <a href="msaterm.html#M2">CompoundTerm</a> of <font color="Maroon">S</font>,<font color="Maroon">V</font>
 
<b>by </b><i>, <a class="ref" href="msaterm.html#T28">MSATERM:28</a>, <a class="ref" href="msaterm.html#D6">MSATERM:def 6</a></i>;<br/>
<b>hence </b><a NAME="E7:5"/>
<font color="Maroon">X</font> is    <a href="msaterm.html#M3">SetWithCompoundTerm</a> of <font color="Maroon">S</font>,<font color="Maroon">V</font>
 <b>by </b><i><a class="ref" href="msaterm.html#D7">MSATERM:def 7</a></i>;<br/>


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