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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>set </b><font color="Maroon">T</font> = <font color="Maroon">S</font> <a href="msaterm.html#K1" target="_self">-Terms</a> <font color="Maroon">V</font>;<br/>
<b>set </b><font color="Maroon">X</font> = <font color="Maroon">V</font>;<br/>
<a NAME="E1:34"/><i><font color="Green">E26</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="msafree.html#K8">FreeSort</a> <font color="Maroon">V</font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font>
 
<b>by </b><i><a class="ref" href="pboole.html#D3">PBOOLE:def 3</a></i>;<br/>
<div><b>hereby </b> <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a>,<a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a>
<div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:34_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">S</font> <a href="msaterm.html#K1" target="_self">-Terms</a> <font color="Maroon">V</font>
 ;<br/><b>then reconsider </b><font color="Maroon">t</font> = <font color="Maroon">x</font> as   <a href="msaterm.html#NM1">Term</a> of <font color="Maroon">S</font>,<font color="Maroon">V</font> ;<br/><b>consider </b><font color="Maroon">s</font> being   <a href="msualg_1.html#NM1">SortSymbol</a> of <font color="Maroon">S</font><b> such that </b><br/><a NAME="E4:34_1"/><i><font color="Green">E27</font></i>: 
<font color="Maroon">t</font> <a href="hidden.html#R2">in</a>  <a href="msafree.html#K7">FreeSort</a> <font color="Maroon">V</font>,<font color="Maroon">s</font>
 <b>by </b><i/>;<br/><a NAME="E5:34_1"/>
 <a href="msafree.html#K7">FreeSort</a> <font color="Maroon">V</font>,<font color="Maroon">s</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="msafree.html#K8">FreeSort</a> <font color="Maroon">V</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">s</font>
 <b>by </b><i><a class="ref" href="msafree.html#D13">MSAFREE:def 13</a></i>;<br/><b>hence </b><a NAME="E6:34_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="card_3.html#K3">Union</a> <span class="p1">(<span class="default"><a href="msafree.html#K8">FreeSort</a> <font color="Maroon">V</font></span>)</span>
 <b>by </b><i>, , <a class="ref" href="card_5.html#T10">CARD_5:10</a></i>;<br/></div>
<b>end;</b></div>

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E3:34"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="card_3.html#K3">Union</a> <span class="p1">(<span class="default"><a href="msafree.html#K8">FreeSort</a> <font color="Maroon">V</font></span>)</span>
 ;<br/>

<b>then consider </b><font color="Maroon">y</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E5:34"/><i><font color="Green">E28</font></i>: 
( <font color="Maroon">y</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="msafree.html#K8">FreeSort</a> <font color="Maroon">V</font></span>)</span> &amp; <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="msafree.html#K8">FreeSort</a> <font color="Maroon">V</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">y</font> )
 <b>by </b><i><a class="ref" href="card_5.html#T10">CARD_5:10</a></i>;<br/>
<b>reconsider </b><font color="Maroon">y</font> = <font color="Maroon">y</font> as   <a href="msualg_1.html#NM1">SortSymbol</a> of <font color="Maroon">S</font> <b>by </b><i>, <a class="ref" href="pboole.html#D3">PBOOLE:def 3</a></i>;<br/>
<a NAME="E7:34"/>
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="msafree.html#K7">FreeSort</a> <font color="Maroon">V</font>,<font color="Maroon">y</font> &amp;  <a href="msafree.html#K7">FreeSort</a> <font color="Maroon">V</font>,<font color="Maroon">y</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">S</font> <a href="msaterm.html#K1" target="_self">-Terms</a> <font color="Maroon">V</font> )
 
<b>by </b><i>, <a class="ref" href="msafree.html#D13">MSAFREE:def 13</a></i>;<br/>
<b>hence </b><a NAME="E8:34"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">S</font> <a href="msaterm.html#K1" target="_self">-Terms</a> <font color="Maroon">V</font>
 ;<br/>


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