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<b>let </b><font color="Maroon">F</font> be   <a href="msualg_3.html#NM1">ManySortedFunction</a> of <font color="Maroon">U1</font>,<span class="p1">(<span class="default"><a href="osalg_4.html#K16" target="_self">QuotOSAlg</a> <font color="Maroon">U1</font>,<font color="Maroon">R</font></span>)</span>, <font color="Maroon">G</font> be   <a href="msualg_3.html#NM1">ManySortedFunction</a> of <font color="Maroon">U1</font>,<span class="p1">(<span class="default"><a href="osalg_4.html#K16" target="_self">QuotOSAlg</a> <font color="Maroon">U1</font>,<font color="Maroon">R</font></span>)</span>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:50_1_2"/><i><font color="Green">E44</font></i>: 
for <font color="Olive">s</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">S</font> holds  <font color="Maroon">F</font> <a href="msualg_3.html#K1">.</a> <font color="Olive">s</font> <a href="funct_2.html#R1">=</a>  <a href="osalg_4.html#K17" target="_self">OSNat_Hom</a> <font color="Maroon">U1</font>,<font color="Maroon">R</font>,<font color="Olive">s</font>
 <b>and </b><br/><a NAME="E2:50_1_2"/><i><font color="Green">E45</font></i>: 
for <font color="Olive">s</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">S</font> holds  <font color="Maroon">G</font> <a href="msualg_3.html#K1">.</a> <font color="Olive">s</font> <a href="funct_2.html#R1">=</a>  <a href="osalg_4.html#K17" target="_self">OSNat_Hom</a> <font color="Maroon">U1</font>,<font color="Maroon">R</font>,<font color="Olive">s</font>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="50_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">i</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:50_1_2_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">s</font> = <font color="Maroon">i</font> as   <a href="osalg_1.html#NM1">SortSymbol</a> of <font color="Maroon">S</font> ;<br/><a NAME="E3:50_1_2_1"/>
( <font color="Maroon">F</font> <a href="msualg_3.html#K1">.</a> <font color="Maroon">s</font> <a href="funct_2.html#R1">=</a>  <a href="osalg_4.html#K17" target="_self">OSNat_Hom</a> <font color="Maroon">U1</font>,<font color="Maroon">R</font>,<font color="Maroon">s</font> &amp; <font color="Maroon">G</font> <a href="msualg_3.html#K1">.</a> <font color="Maroon">s</font> <a href="funct_2.html#R1">=</a>  <a href="osalg_4.html#K17" target="_self">OSNat_Hom</a> <font color="Maroon">U1</font>,<font color="Maroon">R</font>,<font color="Maroon">s</font> )
 <b>by </b><i>, </i>;<br/><b>hence </b><a NAME="E4:50_1_2_1"/>
<font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">G</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:50_1_2"/>
<font color="Maroon">F</font> <a href="hidden.html#R1">=</a> <font color="Maroon">G</font>
 <b>by </b><i><a class="ref" href="pboole.html#T3">PBOOLE:3</a></i>;<br/>


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