<?xml version="1.0"?>
<div class="add">

<b>set </b><font color="Maroon">O</font> = <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">f</font>,<font color="Olive">p</font></span><a href="tarski.html#K4">]</a></span> where <font color="Olive">f</font> is   <a href="pua2mss1.html#NM2">OperSymbol</a> of <font color="Maroon">A</font>, <font color="Olive">p</font> is    <a href="finseq_2.html#M2">Element</a> of <font color="Maroon">P</font> <a href="finseq_2.html#K3">*</a>  :  <a href="card_3.html#K4">product</a> <font color="Olive">p</font> <a href="subset_1.html#R2">meets</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="pua2mss1.html#K2" target="_self">Den</a> <font color="Olive">f</font>,<font color="Maroon">A</font></span>)</span> </span>}</span> ;<br/>
<b>let </b><font color="Maroon">S1</font> be  <a href="msualg_1.html#V1">strict</a>  <a href="msualg_1.html#L1">ManySortedSign</a> , <font color="Maroon">S2</font> be  <a href="msualg_1.html#V1">strict</a>  <a href="msualg_1.html#L1">ManySortedSign</a> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:66_1_2"/><i><font color="Green">E78</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">P</font>
 <b>and </b><br/><a NAME="E2:66_1_2"/><i><font color="Green">E126</font></i>: 
the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">S1</font> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">f</font>,<font color="Olive">p</font></span><a href="tarski.html#K4">]</a></span> where <font color="Olive">f</font> is   <a href="pua2mss1.html#NM2">OperSymbol</a> of <font color="Maroon">A</font>, <font color="Olive">p</font> is    <a href="finseq_2.html#M2">Element</a> of <font color="Maroon">P</font> <a href="finseq_2.html#K3">*</a>  :  <a href="card_3.html#K4">product</a> <font color="Olive">p</font> <a href="subset_1.html#R2">meets</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="pua2mss1.html#K2" target="_self">Den</a> <font color="Olive">f</font>,<font color="Maroon">A</font></span>)</span> </span>}</span> 
 <b>and </b><br/><a NAME="E3:66_1_2"/><i><font color="Green">E127</font></i>: 
for <font color="Olive">f</font> being  <a href="pua2mss1.html#NM2">OperSymbol</a> of <font color="Maroon">A</font><br/> for <font color="Olive">p</font> being   <a href="finseq_2.html#M2">Element</a> of <font color="Maroon">P</font> <a href="finseq_2.html#K3">*</a>   st  <a href="card_3.html#K4">product</a> <font color="Olive">p</font> <a href="subset_1.html#R2">meets</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="pua2mss1.html#K2" target="_self">Den</a> <font color="Olive">f</font>,<font color="Maroon">A</font></span>)</span> holds <br/>( the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">S1</font> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">f</font>,<font color="Olive">p</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R1">=</a> <font color="Olive">p</font> &amp; <span class="p1">(<span class="default"><a href="pua2mss1.html#K2" target="_self">Den</a> <font color="Olive">f</font>,<font color="Maroon">A</font></span>)</span> <a href="relset_1.html#K10">.:</a> <span class="p1">(<span class="default"><a href="card_3.html#K4">product</a> <font color="Olive">p</font></span>)</span> <a href="tarski.html#R1">c=</a> the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">S1</font> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">f</font>,<font color="Olive">p</font></span><a href="tarski.html#K4">]</a></span> )
 <b>and </b><br/><a NAME="E4:66_1_2"/><i><font color="Green">E130</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">P</font>
 <b>and </b><br/><a NAME="E5:66_1_2"/><i><font color="Green">E131</font></i>: 
the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">S2</font> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">f</font>,<font color="Olive">p</font></span><a href="tarski.html#K4">]</a></span> where <font color="Olive">f</font> is   <a href="pua2mss1.html#NM2">OperSymbol</a> of <font color="Maroon">A</font>, <font color="Olive">p</font> is    <a href="finseq_2.html#M2">Element</a> of <font color="Maroon">P</font> <a href="finseq_2.html#K3">*</a>  :  <a href="card_3.html#K4">product</a> <font color="Olive">p</font> <a href="subset_1.html#R2">meets</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="pua2mss1.html#K2" target="_self">Den</a> <font color="Olive">f</font>,<font color="Maroon">A</font></span>)</span> </span>}</span> 
 <b>and </b><br/><a NAME="E6:66_1_2"/><i><font color="Green">E132</font></i>: 
for <font color="Olive">f</font> being  <a href="pua2mss1.html#NM2">OperSymbol</a> of <font color="Maroon">A</font><br/> for <font color="Olive">p</font> being   <a href="finseq_2.html#M2">Element</a> of <font color="Maroon">P</font> <a href="finseq_2.html#K3">*</a>   st  <a href="card_3.html#K4">product</a> <font color="Olive">p</font> <a href="subset_1.html#R2">meets</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="pua2mss1.html#K2" target="_self">Den</a> <font color="Olive">f</font>,<font color="Maroon">A</font></span>)</span> holds <br/>( the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">S2</font> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">f</font>,<font color="Olive">p</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R1">=</a> <font color="Olive">p</font> &amp; <span class="p1">(<span class="default"><a href="pua2mss1.html#K2" target="_self">Den</a> <font color="Olive">f</font>,<font color="Maroon">A</font></span>)</span> <a href="relset_1.html#K10">.:</a> <span class="p1">(<span class="default"><a href="card_3.html#K4">product</a> <font color="Olive">p</font></span>)</span> <a href="tarski.html#R1">c=</a> the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">S2</font> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">f</font>,<font color="Olive">p</font></span><a href="tarski.html#K4">]</a></span> )
 ;<br/>

<a NAME="E7:66_1_2"/><i><font color="Green">E133</font></i>: 
(  <a href="relset_1.html#K4">dom</a> the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">S1</font> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">f</font>,<font color="Olive">p</font></span><a href="tarski.html#K4">]</a></span> where <font color="Olive">f</font> is   <a href="pua2mss1.html#NM2">OperSymbol</a> of <font color="Maroon">A</font>, <font color="Olive">p</font> is    <a href="finseq_2.html#M2">Element</a> of <font color="Maroon">P</font> <a href="finseq_2.html#K3">*</a>  :  <a href="card_3.html#K4">product</a> <font color="Olive">p</font> <a href="subset_1.html#R2">meets</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="pua2mss1.html#K2" target="_self">Den</a> <font color="Olive">f</font>,<font color="Maroon">A</font></span>)</span> </span>}</span>  &amp;  <a href="relset_1.html#K4">dom</a> the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">S2</font> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">f</font>,<font color="Olive">p</font></span><a href="tarski.html#K4">]</a></span> where <font color="Olive">f</font> is   <a href="pua2mss1.html#NM2">OperSymbol</a> of <font color="Maroon">A</font>, <font color="Olive">p</font> is    <a href="finseq_2.html#M2">Element</a> of <font color="Maroon">P</font> <a href="finseq_2.html#K3">*</a>  :  <a href="card_3.html#K4">product</a> <font color="Olive">p</font> <a href="subset_1.html#R2">meets</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="pua2mss1.html#K2" target="_self">Den</a> <font color="Olive">f</font>,<font color="Maroon">A</font></span>)</span> </span>}</span>  )
 
<b>by </b><i>, , <a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="66_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">o</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:66_1_2_1"/>
<font color="Maroon">o</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">f</font>,<font color="Olive">p</font></span><a href="tarski.html#K4">]</a></span> where <font color="Olive">f</font> is   <a href="pua2mss1.html#NM2">OperSymbol</a> of <font color="Maroon">A</font>, <font color="Olive">p</font> is    <a href="finseq_2.html#M2">Element</a> of <font color="Maroon">P</font> <a href="finseq_2.html#K3">*</a>  :  <a href="card_3.html#K4">product</a> <font color="Olive">p</font> <a href="subset_1.html#R2">meets</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="pua2mss1.html#K2" target="_self">Den</a> <font color="Olive">f</font>,<font color="Maroon">A</font></span>)</span> </span>}</span> 
 ;<br/><b>then consider </b><font color="Maroon">f</font> being   <a href="pua2mss1.html#NM2">OperSymbol</a> of <font color="Maroon">A</font>, <font color="Maroon">p</font> being    <a href="finseq_2.html#M2">Element</a> of <font color="Maroon">P</font> <a href="finseq_2.html#K3">*</a> <b> such that </b><br/><a NAME="E3:66_1_2_1"/><i><font color="Green">E134</font></i>: 
( <font color="Maroon">o</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">f</font>,<font color="Maroon">p</font></span><a href="tarski.html#K4">]</a></span> &amp;  <a href="card_3.html#K4">product</a> <font color="Maroon">p</font> <a href="subset_1.html#R2">meets</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="pua2mss1.html#K2" target="_self">Den</a> <font color="Maroon">f</font>,<font color="Maroon">A</font></span>)</span> )
 ;<br/><b>thus </b>the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">S1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">o</font> = 
<font color="Maroon">p</font>
<b>by </b><i>, </i>
<br/>.= 
the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">S2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">o</font>
<b>by </b><i>, </i>
;<br/></div><b>end;</b></div>
<a NAME="E9:66_1_2"/><b>then </b><i><font color="Green">E135</font></i>: 
the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">S1</font> <a href="funct_2.html#R1">=</a> the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">S2</font>
 
<b>by </b><i>, <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/>
<a NAME="E10:66_1_2"/><i><font color="Green">E136</font></i>: 
(  <a href="relset_1.html#K4">dom</a> the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">S1</font> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">f</font>,<font color="Olive">p</font></span><a href="tarski.html#K4">]</a></span> where <font color="Olive">f</font> is   <a href="pua2mss1.html#NM2">OperSymbol</a> of <font color="Maroon">A</font>, <font color="Olive">p</font> is    <a href="finseq_2.html#M2">Element</a> of <font color="Maroon">P</font> <a href="finseq_2.html#K3">*</a>  :  <a href="card_3.html#K4">product</a> <font color="Olive">p</font> <a href="subset_1.html#R2">meets</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="pua2mss1.html#K2" target="_self">Den</a> <font color="Olive">f</font>,<font color="Maroon">A</font></span>)</span> </span>}</span>  &amp;  <a href="relset_1.html#K4">dom</a> the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">S2</font> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">f</font>,<font color="Olive">p</font></span><a href="tarski.html#K4">]</a></span> where <font color="Olive">f</font> is   <a href="pua2mss1.html#NM2">OperSymbol</a> of <font color="Maroon">A</font>, <font color="Olive">p</font> is    <a href="finseq_2.html#M2">Element</a> of <font color="Maroon">P</font> <a href="finseq_2.html#K3">*</a>  :  <a href="card_3.html#K4">product</a> <font color="Olive">p</font> <a href="subset_1.html#R2">meets</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="pua2mss1.html#K2" target="_self">Den</a> <font color="Olive">f</font>,<font color="Maroon">A</font></span>)</span> </span>}</span>  )
 
<b>by </b><i><a class="ref" href="pua2mss1.html#T1" target="_self">Th1</a>, , , , <a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<b>consider </b><font color="Maroon">R</font> being   <a href="eqrel_1.html#NM2">Equivalence_Relation</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">A</font><b> such that </b><br/><a NAME="E12:66_1_2"/><i><font color="Green">E137</font></i>: 
<font color="Maroon">P</font> <a href="hidden.html#R1">=</a>  <a href="eqrel_1.html#K9">Class</a> <font color="Maroon">R</font>
 <b>by </b><i><a class="ref" href="eqrel_1.html#T43">EQREL_1:43</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="66_1_2_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">o</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:66_1_2_2"/><i><font color="Green">E138</font></i>: 
<font color="Maroon">o</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">f</font>,<font color="Olive">p</font></span><a href="tarski.html#K4">]</a></span> where <font color="Olive">f</font> is   <a href="pua2mss1.html#NM2">OperSymbol</a> of <font color="Maroon">A</font>, <font color="Olive">p</font> is    <a href="finseq_2.html#M2">Element</a> of <font color="Maroon">P</font> <a href="finseq_2.html#K3">*</a>  :  <a href="card_3.html#K4">product</a> <font color="Olive">p</font> <a href="subset_1.html#R2">meets</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="pua2mss1.html#K2" target="_self">Den</a> <font color="Olive">f</font>,<font color="Maroon">A</font></span>)</span> </span>}</span> 
 ;<br/><b>then consider </b><font color="Maroon">f</font> being   <a href="pua2mss1.html#NM2">OperSymbol</a> of <font color="Maroon">A</font>, <font color="Maroon">p</font> being    <a href="finseq_2.html#M2">Element</a> of <font color="Maroon">P</font> <a href="finseq_2.html#K3">*</a> <b> such that </b><br/><a NAME="E3:66_1_2_2"/><i><font color="Green">E139</font></i>: 
( <font color="Maroon">o</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">f</font>,<font color="Maroon">p</font></span><a href="tarski.html#K4">]</a></span> &amp;  <a href="card_3.html#K4">product</a> <font color="Maroon">p</font> <a href="subset_1.html#R2">meets</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="pua2mss1.html#K2" target="_self">Den</a> <font color="Maroon">f</font>,<font color="Maroon">A</font></span>)</span> )
 ;<br/><b>consider </b><font color="Maroon">x</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E5:66_1_2_2"/><i><font color="Green">E140</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="card_3.html#K4">product</a> <font color="Maroon">p</font> &amp; <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="pua2mss1.html#K2" target="_self">Den</a> <font color="Maroon">f</font>,<font color="Maroon">A</font></span>)</span> )
 <b>by </b><i>, <a class="ref" href="xboole_0.html#T3">XBOOLE_0:3</a></i>;<br/><a NAME="E6:66_1_2_2"/>
( <span class="p1">(<span class="default"><a href="pua2mss1.html#K2" target="_self">Den</a> <font color="Maroon">f</font>,<font color="Maroon">A</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="pua2mss1.html#K2" target="_self">Den</a> <font color="Maroon">f</font>,<font color="Maroon">A</font></span>)</span> <a href="relset_1.html#K10">.:</a> <span class="p1">(<span class="default"><a href="card_3.html#K4">product</a> <font color="Maroon">p</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="pua2mss1.html#K2" target="_self">Den</a> <font color="Maroon">f</font>,<font color="Maroon">A</font></span>)</span> <a href="relset_1.html#K10">.:</a> <span class="p1">(<span class="default"><a href="card_3.html#K4">product</a> <font color="Maroon">p</font></span>)</span> <a href="tarski.html#R1">c=</a> the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">S1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">o</font> &amp; <span class="p1">(<span class="default"><a href="pua2mss1.html#K2" target="_self">Den</a> <font color="Maroon">f</font>,<font color="Maroon">A</font></span>)</span> <a href="relset_1.html#K10">.:</a> <span class="p1">(<span class="default"><a href="card_3.html#K4">product</a> <font color="Maroon">p</font></span>)</span> <a href="tarski.html#R1">c=</a> the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">S2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">o</font> &amp; the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">S1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">o</font> <a href="hidden.html#R2">in</a> <font color="Maroon">P</font> &amp; the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">S2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">o</font> <a href="hidden.html#R2">in</a> <font color="Maroon">P</font> )
 <b>by </b><i><a class="ref" href="pua2mss1.html#T1" target="_self">Th1</a>, , , , , , , , , <a class="ref" href="funct_1.html#D12">FUNCT_1:def 12</a>, <a class="ref" href="funct_2.html#T7">FUNCT_2:7</a></i>;<br/><a NAME="E7:66_1_2_2"/><b>then </b>
( <span class="p1">(<span class="default"><a href="pua2mss1.html#K2" target="_self">Den</a> <font color="Maroon">f</font>,<font color="Maroon">A</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">S1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">o</font> &amp; <span class="p1">(<span class="default"><a href="pua2mss1.html#K2" target="_self">Den</a> <font color="Maroon">f</font>,<font color="Maroon">A</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">S2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">o</font> &amp;  ex <font color="Olive">y</font> being   <a href="hidden.html#M1">set</a>  st <br/>( <font color="Olive">y</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">A</font> &amp; the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">S1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">o</font> <a href="hidden.html#R1">=</a>  <a href="eqrel_1.html#K7">Class</a> <font color="Maroon">R</font>,<font color="Olive">y</font> ) &amp;  ex <font color="Olive">y</font> being   <a href="hidden.html#M1">set</a>  st <br/>( <font color="Olive">y</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">A</font> &amp; the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">S2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">o</font> <a href="hidden.html#R1">=</a>  <a href="eqrel_1.html#K7">Class</a> <font color="Maroon">R</font>,<font color="Olive">y</font> ) )
 <b>by </b><i>, <a class="ref" href="eqrel_1.html#D5">EQREL_1:def 5</a></i>;<br/><a NAME="E8:66_1_2_2"/><b>then </b>
( the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">S1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">o</font> <a href="hidden.html#R1">=</a>  <a href="eqrel_1.html#K7">Class</a> <font color="Maroon">R</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pua2mss1.html#K2" target="_self">Den</a> <font color="Maroon">f</font>,<font color="Maroon">A</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font></span>)</span> &amp; the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">S2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">o</font> <a href="hidden.html#R1">=</a>  <a href="eqrel_1.html#K7">Class</a> <font color="Maroon">R</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pua2mss1.html#K2" target="_self">Den</a> <font color="Maroon">f</font>,<font color="Maroon">A</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font></span>)</span> )
 <b>by </b><i><a class="ref" href="eqrel_1.html#T31">EQREL_1:31</a></i>;<br/><b>hence </b><a NAME="E9:66_1_2_2"/>
the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">S1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">o</font> <a href="hidden.html#R1">=</a> the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">S2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">o</font>
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E14:66_1_2"/>
<font color="Maroon">S1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">S2</font>
 <b>by </b><i><a class="ref" href="pua2mss1.html#T1" target="_self">Th1</a>, , , , , <a class="ref" href="pua2mss1.html#T2" target="_self">Th2</a>, <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/>


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