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<b>let </b><font color="Maroon">S</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">A</font> be  <a href="relat_1.html#V2">V3</a>  <a href="pboole.html#M1">ManySortedSet</a> of <font color="Maroon">S</font>;<br/><b>let </b><font color="Maroon">R</font> be   <a href="msualg_4.html#NM3">ManySortedRelation</a> of <font color="Maroon">A</font>, <font color="Maroon">E</font> be   <a href="msualg_4.html#NM3">ManySortedRelation</a> of <font color="Maroon">A</font>;<br/>





<b>assume </b><a NAME="E1:78"/><i><font color="Green">E32</font></i>: 
for <font color="Olive">s</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">S</font><br/> for <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">A</font> <a href="funct_1.html#K1">.</a> <font color="Olive">s</font> holds <br/> ( <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">a</font>,<font color="Olive">b</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">E</font> <a href="msualg_4.html#K1">.</a> <font color="Olive">s</font> iff <font color="Olive">a</font>,<font color="Olive">b</font> <a href="rewrite1.html#R2">are_convertible_wrt</a> <font color="Maroon">R</font> <a href="msualg_4.html#K1">.</a> <font color="Olive">s</font> )
 ;<br/>

<b>let </b><font color="Maroon">i</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="msualg_4.html#D3">MSUALG_4:def 3</a><br/><b>let </b><font color="Maroon">P</font> be   <a href="relset_1.html#NM3">Relation</a> of <font color="Maroon">A</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>;<br/>



<b>assume </b><a NAME="E2:78"/>
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a> <font color="Maroon">S</font>
 ;<br/>

<b>then reconsider </b><font color="Maroon">s</font> = <font color="Maroon">i</font> as    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">S</font> ;<br/>
<a NAME="E4:78"/>
for <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">s</font> &amp; <font color="Olive">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">s</font> holds <br/>( <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">a</font>,<font color="Olive">b</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">E</font> <a href="msualg_4.html#K1">.</a> <font color="Maroon">s</font> iff <font color="Olive">a</font>,<font color="Olive">b</font> <a href="rewrite1.html#R2">are_convertible_wrt</a> <font color="Maroon">R</font> <a href="msualg_4.html#K1">.</a> <font color="Maroon">s</font> )
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E5:78"/>
(  not <font color="Maroon">E</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">P</font> or <font color="Maroon">P</font> is    <a href="relset_1.html#M2">Relation</a> of <font color="Maroon">A</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>,<font color="Maroon">A</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> )
 <b>by </b><i><a class="ref" href="msualg_6.html#T2" target="_self">Th2</a></i>;<br/>


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