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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#NM3">ManySortedRelation</a> of the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>





<a NAME="E1:63"/>
<font color="Maroon">c<sub>3</sub></font> <a href="pboole.html#R2">c=</a>  <a href="msualg_6.html#K8" target="_self">TRS</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="msualg_6.html#D13" target="_self">Def13</a></i>;<br/>
<a NAME="E2:63"/><b>then </b>
 <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#K8" target="_self">TRS</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="msualg_6.html#D12" target="_self">Def12</a></i>;<br/>
<b>hence </b><a NAME="E3:63"/>
 <a href="msualg_6.html#K6" target="_self">InvCl</a> <span class="p1">(<span class="default"><a href="msualg_6.html#K7" target="_self">StabCl</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="pboole.html#R2">c=</a>  <a href="msualg_6.html#K8" target="_self">TRS</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="ref" href="msualg_6.html#D11" target="_self">Def11</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="pboole.html#D13">PBOOLE:def 13</a><br/>

<a NAME="E4:63"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="pboole.html#R2">c=</a>  <a href="msualg_6.html#K7" target="_self">StabCl</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#K6" target="_self">InvCl</a> <span class="p1">(<span class="default"><a href="msualg_6.html#K7" target="_self">StabCl</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> )
 
<b>by </b><i><a class="ref" href="msualg_6.html#D11" target="_self">Def11</a>, <a class="ref" href="msualg_6.html#D12" target="_self">Def12</a></i>;<br/>
<a NAME="E5:63"/><b>then </b>
(  <a href="msualg_6.html#K6" target="_self">InvCl</a> <span class="p1">(<span class="default"><a href="msualg_6.html#K7" target="_self">StabCl</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> is  <a href="msualg_6.html#V3" target="_self">invariant</a> <a href="msualg_6.html#V4" target="_self">stable</a> <a href="msualg_4.html#NM4">ManySortedRelation</a> of <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="pboole.html#R2">c=</a>  <a href="msualg_6.html#K6" target="_self">InvCl</a> <span class="p1">(<span class="default"><a href="msualg_6.html#K7" target="_self">StabCl</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> )
 
<b>by </b><i><a class="ref" href="msualg_6.html#T30" target="_self">Th30</a>, <a class="ref" href="pboole.html#T15">PBOOLE:15</a></i>;<br/>
<b>hence </b><a NAME="E6:63"/>
 <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#K6" target="_self">InvCl</a> <span class="p1">(<span class="default"><a href="msualg_6.html#K7" target="_self">StabCl</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="msualg_6.html#D13" target="_self">Def13</a></i>;<br/>


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