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<b>deffunc </b><font color="Maroon">H<sub>1</sub></font>(  <a href="msualg_1.html#NM1">SortSymbol</a> of <font color="Maroon">S</font>) <b>-&gt; </b>   <a href="hidden.html#M1">set</a>  = <span class="p1">{<span class="default"> <font color="Olive">t</font> where <font color="Olive">t</font> is   <a href="msaterm.html#NM1">Term</a> of <font color="Maroon">S</font>,<font color="Maroon">Y</font> : (  <a href="msaterm.html#K7">the_sort_of</a> <font color="Olive">t</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a<sub>1</sub></font> &amp;  <a href="msafree3.html#K4" target="_self">variables_in</a> <font color="Olive">t</font> <a href="pboole.html#R2">c=</a> <font color="Maroon">X</font> ) </span>}</span> ;<br/>
<b>consider </b><font color="Maroon">T</font> being    <a href="pboole.html#M1">ManySortedSet</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font><b> such that </b><br/><a NAME="E2:27_1_1"/><i><font color="Green">E42</font></i>: 
for <font color="Olive">s</font> being  <a href="msualg_1.html#NM1">SortSymbol</a> of <font color="Maroon">S</font> holds  <font color="Maroon">T</font> <a href="funct_1.html#K1">.</a> <font color="Olive">s</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">s</font>)
 <b>from </b><i><a class="ref" href="pboole.html#S5">PBOOLE:sch 5</a>();<br/></i>
<a NAME="E3:27_1_1"/>
<font color="Maroon">T</font> <a href="pboole.html#R2">c=</a> the <a href="msualg_1.html#U4">Sorts</a> of <span class="p1">(<span class="default"><a href="msafree.html#K11">FreeMSA</a> <font color="Maroon">Y</font></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="27_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">s</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="pboole.html#D5">PBOOLE:def 5</a><br/>

<b>assume </b><a NAME="E1:27_1_1_1"/>
<font color="Maroon">s</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font>
 ;<br/>

<b>then reconsider </b><font color="Maroon">s'</font> = <font color="Maroon">s</font> as   <a href="msualg_1.html#NM1">SortSymbol</a> of <font color="Maroon">S</font> ;<br/>
<a NAME="E3:27_1_1_1"/><i><font color="Green">E47</font></i>: 
<font color="Maroon">T</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">s'</font> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <font color="Olive">t</font> where <font color="Olive">t</font> is   <a href="msaterm.html#NM1">Term</a> of <font color="Maroon">S</font>,<font color="Maroon">Y</font> : (  <a href="msaterm.html#K7">the_sort_of</a> <font color="Olive">t</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s'</font> &amp;  <a href="msafree3.html#K4" target="_self">variables_in</a> <font color="Olive">t</font> <a href="pboole.html#R2">c=</a> <font color="Maroon">X</font> ) </span>}</span> 
 
<b>by </b><i/>;<br/>
<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="E4:27_1_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">T</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">s</font>
 ;<br/>

<a NAME="E5:27_1_1_1"/><b>then </b>
 ex <font color="Olive">t</font> being  <a href="msaterm.html#NM1">Term</a> of <font color="Maroon">S</font>,<font color="Maroon">Y</font> st <br/>( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Olive">t</font> &amp;  <a href="msaterm.html#K7">the_sort_of</a> <font color="Olive">t</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s'</font> &amp;  <a href="msafree3.html#K4" target="_self">variables_in</a> <font color="Olive">t</font> <a href="pboole.html#R2">c=</a> <font color="Maroon">X</font> )
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E6:27_1_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> the <a href="msualg_1.html#U4">Sorts</a> of <span class="p1">(<span class="default"><a href="msafree.html#K11">FreeMSA</a> <font color="Maroon">Y</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">s</font>
 <b>by </b><i/>;<br/>


</div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon">T</font> = <font color="Maroon">T</font> as   <a href="msualg_2.html#NM1">MSSubset</a> of <span class="p1">(<span class="default"><a href="msafree.html#K11">FreeMSA</a> <font color="Maroon">Y</font></span>)</span> <b>by </b><i><a class="ref" href="pboole.html#D23">PBOOLE:def 23</a></i>;<br/>
<b>take </b>
<font color="Maroon">T</font>
;<br/>

<b>thus </b><a NAME="E5:27_1_1"/>
for <font color="Olive">s</font> being  <a href="msualg_1.html#NM1">SortSymbol</a> of <font color="Maroon">S</font> holds  <font color="Maroon">T</font> <a href="funct_1.html#K1">.</a> <font color="Olive">s</font> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <font color="Olive">t</font> where <font color="Olive">t</font> is   <a href="msaterm.html#NM1">Term</a> of <font color="Maroon">S</font>,<font color="Maroon">Y</font> : (  <a href="msaterm.html#K7">the_sort_of</a> <font color="Olive">t</font> <a href="hidden.html#R1">=</a> <font color="Olive">s</font> &amp;  <a href="msafree3.html#K4" target="_self">variables_in</a> <font color="Olive">t</font> <a href="pboole.html#R2">c=</a> <font color="Maroon">X</font> ) </span>}</span> 
 <b>by </b><i/>;<br/>


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