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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="struct_0.html#V3">empty</a> non <a href="msualg_1.html#V2">void</a>  <a href="msualg_1.html#L1">ManySortedSign</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be  <a href="msualg_1.html#V5">non-empty</a>  <a href="msualg_1.html#L3">MSAlgebra</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="msualg_4.html#NM4">ManySortedRelation</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>





<a NAME="E1:82"/><i><font color="Green">E56</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="pboole.html#R2">c=</a>  <a href="msualg_6.html#K10" target="_self">EqTh</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="msualg_6.html#D15" target="_self">Def15</a></i>;<br/>
<b>hence </b><a NAME="E2:82"/>
 <a href="msualg_6.html#K9" target="_self">EqCl</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="pboole.html#R2">c=</a>  <a href="msualg_6.html#K10" target="_self">EqTh</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="ref" href="msualg_6.html#T44" target="_self">Th44</a></i>;<br/>

<b>thus </b><a NAME="E3:82"/>
(  <a href="msualg_6.html#K6" target="_self">InvCl</a> <font color="Maroon">c<sub>3</sub></font> <a href="pboole.html#R2">c=</a>  <a href="msualg_6.html#K10" target="_self">EqTh</a> <font color="Maroon">c<sub>3</sub></font> &amp;  <a href="msualg_6.html#K7" target="_self">StabCl</a> <font color="Maroon">c<sub>3</sub></font> <a href="pboole.html#R2">c=</a>  <a href="msualg_6.html#K10" target="_self">EqTh</a> <font color="Maroon">c<sub>3</sub></font> &amp;  <a href="msualg_6.html#K8" target="_self">TRS</a> <font color="Maroon">c<sub>3</sub></font> <a href="pboole.html#R2">c=</a>  <a href="msualg_6.html#K10" target="_self">EqTh</a> <font color="Maroon">c<sub>3</sub></font> )
 <b>by </b><i><a class="txt" href="msualg_6.html#E1:82"><i><font color="Green">E56</font></i></a>, <a class="ref" href="msualg_6.html#D11" target="_self">Def11</a>, <a class="ref" href="msualg_6.html#D12" target="_self">Def12</a>, <a class="ref" href="msualg_6.html#D13" target="_self">Def13</a></i>;<br/>


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