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

<b>reconsider </b><font color="Maroon">Q</font> =  <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">R</font></span>)</span> as  <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">A</font> <b>by </b><i/>;<br/>
<b>take </b>
<font color="Maroon">Q</font>
;<br/>

<a NAME="E2:57_1_2"/>
( <font color="Maroon">R</font> <a href="pboole.html#R2">c=</a>  <a href="msualg_6.html#K7" target="_self">StabCl</a> <font color="Maroon">R</font> &amp;  <a href="msualg_6.html#K7" target="_self">StabCl</a> <font color="Maroon">R</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">R</font></span>)</span> )
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E3:57_1_2"/>
<font color="Maroon">R</font> <a href="pboole.html#R2">c=</a> <font color="Maroon">Q</font>
 <b>by </b><i><a class="ref" href="pboole.html#T15">PBOOLE:15</a></i>;<br/>

<b>let </b><font color="Maroon">P</font> be  <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">A</font>;<br/>

<b>assume </b><a NAME="E4:57_1_2"/>
<font color="Maroon">R</font> <a href="pboole.html#R2">c=</a> <font color="Maroon">P</font>
 ;<br/>

<a NAME="E5:57_1_2"/><b>then </b>
 <a href="msualg_6.html#K7" target="_self">StabCl</a> <font color="Maroon">R</font> <a href="pboole.html#R2">c=</a> <font color="Maroon">P</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E6:57_1_2"/>
<font color="Maroon">Q</font> <a href="pboole.html#R2">c=</a> <font color="Maroon">P</font>
 <b>by </b><i/>;<br/>


</div>
