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<b>let </b><font color="Maroon" title="c1">S</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> non <a href="msualg_1.html#V2" title="MSUALG_1:attr.2">void</a>  <a href="msualg_1.html#L1" title="MSUALG_1:struct.1">ManySortedSign</a> ;<br/><b>let </b><font color="Maroon" title="c2">A</font> be  <a href="msualg_1.html#V5" title="MSUALG_1:attr.5">non-empty</a>  <a href="msualg_1.html#L3" title="MSUALG_1:struct.3">MSAlgebra</a> of <font color="Maroon" title="c1">S</font>;<br/><b>let </b><font color="Maroon" title="c3">C</font> be   <a href="msualg_4.html#NM5" title="MSUALG_4:NM.5">MSCongruence</a> of <font color="Maroon" title="c2">A</font>;<br/><b>let </b><font color="Maroon" title="c4">s</font> be   <a href="msualg_1.html#NM1" title="MSUALG_1:NM.1">SortSymbol</a> of <font color="Maroon" title="c1">S</font>;<br/><b>let </b><font color="Maroon" title="c5">a</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <span class="p1">(<span class="default"><a href="msualg_4.html#K14" title="MSUALG_4:func.14">QuotMSAlg</a> <font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">C</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">s</font>;<br/>









<a NAME="E1:43"/>
<font color="Maroon" title="c5">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="msualg_4.html#K4" title="MSUALG_4:func.4">Class</a> <font color="Maroon" title="c3">C</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">s</font>
 
;<br/>
<a NAME="E2:43"/><b>then </b>
<font color="Maroon" title="c5">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="eqrel_1.html#K8" title="EQREL_1:func.8">Class</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">C</font> <a href="msualg_4.html#K2" title="MSUALG_4:func.2">.</a> <font color="Maroon" title="c4">s</font></span>)</span>
 
<b>by </b><i><a class="ref" href="msualg_4.html#D8" title="MSUALG_4:def.8">MSUALG_4:def 8</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c6">t</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E4:43"/><i><font color="Green" title="E17">A1</font></i>: 
<font color="Maroon" title="c6">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c2">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">s</font>
 <b>and </b><br/><a NAME="E5:43"/><i><font color="Green" title="E18">A2</font></i>: 
<font color="Maroon" title="c5">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">C</font> <a href="msualg_4.html#K2" title="MSUALG_4:func.2">.</a> <font color="Maroon" title="c4">s</font></span>)</span>,<font color="Maroon" title="c6">t</font>
 <b>by </b><i><a class="ref" href="eqrel_1.html#D5" title="EQREL_1:def.5">EQREL_1:def 5</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c7">t</font> = <font color="Maroon" title="c6">t</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c2">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">s</font> <b>by </b><i><a class="txt" href="msualg_9.html#E4:43"><i><font color="Green" title="E17">A1</font></i></a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c7">t</font>
;<br/>

<b>thus </b><a NAME="E7:43"/>
<font color="Maroon" title="c5">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="msualg_4.html#K3" title="MSUALG_4:func.3">Class</a> <font color="Maroon" title="c3">C</font>,<font color="Maroon" title="c7">t</font>
 <b>by </b><i><a class="txt" href="msualg_9.html#E5:43"><i><font color="Green" title="E18">A2</font></i></a></i>;<br/>


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