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<b>let </b><font color="Maroon">R</font> be   <a href="msualg_4.html#NM4">ManySortedRelation</a> of <font color="Maroon">A</font>;<br/>

<b>assume </b><a NAME="E1:47_1_1"/><i><font color="Green">E32</font></i>: 
for <font color="Olive">i</font> being   <a href="hidden.html#M1">set</a> <br/> for <font color="Olive">P</font> being  <a href="relset_1.html#NM3">Relation</a> of the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A</font> <a href="funct_1.html#K1">.</a> <font color="Olive">i</font>  st <font color="Olive">i</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font> &amp; <font color="Maroon">R</font> <a href="funct_1.html#K1">.</a> <font color="Olive">i</font> <a href="hidden.html#R1">=</a> <font color="Olive">P</font> holds <br/><font color="Olive">P</font> is   <a href="eqrel_1.html#NM2">Equivalence_Relation</a> of the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A</font> <a href="funct_1.html#K1">.</a> <font color="Olive">i</font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="msualg_4.html#D3">MSUALG_4:def 3</a>,<a class="ref" href="msualg_4.html#D5">MSUALG_4:def 5</a><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="pboole.html#D16">PBOOLE:def 16</a><br/>

<b>assume </b><a NAME="E2:47_1_1"/>
<font color="Maroon">i</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">i</font> = <font color="Maroon">i</font> as   <a href="msualg_1.html#NM1">SortSymbol</a> of <font color="Maroon">S</font> ;<br/>
<b>consider </b><font color="Maroon">x</font> being   <a href="msualg_6.html#NM1">Element</a> of <font color="Maroon">A</font>,<font color="Maroon">i</font>;<br/>
<a NAME="E5:47_1_1"/>
<font color="Maroon">R</font> <a href="msualg_4.html#K1">.</a> <font color="Maroon">i</font> is   <a href="eqrel_1.html#NM2">Equivalence_Relation</a> of the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>
 
<b>by </b><i/>;<br/>
<a NAME="E6:47_1_1"/><b>then </b>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">x</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">R</font> <a href="msualg_4.html#K1">.</a> <font color="Maroon">i</font>
 
<b>by </b><i><a class="ref" href="eqrel_1.html#T11">EQREL_1:11</a></i>;<br/>
<b>hence </b><a NAME="E7:47_1_1"/>
not <font color="Maroon">R</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> is <a href="xboole_0.html#V1">empty</a>
 ;<br/>


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