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<b>let </b><font color="Maroon" title="c1">S</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">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">R</font> be   <a href="msualg_4.html#NM4" title="MSUALG_4:NM.4">ManySortedRelation</a> of <font color="Maroon" title="c2">A</font>;<br/>





<a NAME="E1:84"/>
( <font color="Maroon" title="c3">R</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a>  <a href="msualg_6.html#K8" title="MSUALG_6:func.8">TRS</a> <font color="Maroon" title="c3">R</font> &amp;  <a href="msualg_6.html#K8" title="MSUALG_6:func.8">TRS</a> <font color="Maroon" title="c3">R</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a>  <a href="msualg_6.html#K9" title="MSUALG_6:func.9">EqCl</a> <span class="p1">(<span class="default"><a href="msualg_6.html#K8" title="MSUALG_6:func.8">TRS</a> <font color="Maroon" title="c3">R</font></span>)</span>,<font color="Maroon" title="c2">A</font> )
 
<b>by </b><i><a class="ref" href="msualg_6.html#D13" target="_self" title="MSUALG_6:def.13">Def13</a>, <a class="ref" href="msualg_6.html#T43" target="_self" title="MSUALG_6:th.43">Th43</a></i>;<br/>
<a NAME="E2:84"/><b>then </b>
<font color="Maroon" title="c3">R</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a>  <a href="msualg_6.html#K9" title="MSUALG_6:func.9">EqCl</a> <span class="p1">(<span class="default"><a href="msualg_6.html#K8" title="MSUALG_6:func.8">TRS</a> <font color="Maroon" title="c3">R</font></span>)</span>,<font color="Maroon" title="c2">A</font>
 
<b>by </b><i><a class="ref" href="pboole.html#T15" title="PBOOLE:th.15">PBOOLE:15</a></i>;<br/>
<b>hence </b><a NAME="E3:84"/>
 <a href="msualg_6.html#K10" title="MSUALG_6:func.10">EqTh</a> <font color="Maroon" title="c3">R</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a>  <a href="msualg_6.html#K9" title="MSUALG_6:func.9">EqCl</a> <span class="p1">(<span class="default"><a href="msualg_6.html#K8" title="MSUALG_6:func.8">TRS</a> <font color="Maroon" title="c3">R</font></span>)</span>,<font color="Maroon" title="c2">A</font>
 <b>by </b><i><a class="ref" href="msualg_6.html#D15" target="_self" title="MSUALG_6:def.15">Def15</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="pboole.html#D13" title="PBOOLE:def.13">PBOOLE:def 13</a><br/>

<a NAME="E4:84"/>
<font color="Maroon" title="c3">R</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a>  <a href="msualg_6.html#K10" title="MSUALG_6:func.10">EqTh</a> <font color="Maroon" title="c3">R</font>
 
<b>by </b><i><a class="ref" href="msualg_6.html#D15" target="_self" title="MSUALG_6:def.15">Def15</a></i>;<br/>
<a NAME="E5:84"/><b>then </b>
 <a href="msualg_6.html#K8" title="MSUALG_6:func.8">TRS</a> <font color="Maroon" title="c3">R</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a>  <a href="msualg_6.html#K10" title="MSUALG_6:func.10">EqTh</a> <font color="Maroon" title="c3">R</font>
 
<b>by </b><i><a class="ref" href="msualg_6.html#D13" target="_self" title="MSUALG_6:def.13">Def13</a></i>;<br/>
<b>hence </b><a NAME="E6:84"/>
 <a href="msualg_6.html#K9" title="MSUALG_6:func.9">EqCl</a> <span class="p1">(<span class="default"><a href="msualg_6.html#K8" title="MSUALG_6:func.8">TRS</a> <font color="Maroon" title="c3">R</font></span>)</span>,<font color="Maroon" title="c2">A</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a>  <a href="msualg_6.html#K10" title="MSUALG_6:func.10">EqTh</a> <font color="Maroon" title="c3">R</font>
 <b>by </b><i><a class="ref" href="msualg_6.html#T44" target="_self" title="MSUALG_6:th.44">Th44</a></i>;<br/>


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