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<span class="kw">reconsider </span><font color="Maroon" title="c4">Q</font> =  <a href="msualg_6.html#K6" title="MSUALG_6:func.6">InvCl</a> <span class="p1">(<span class="default"><a href="msualg_6.html#K7" title="MSUALG_6:func.7">StabCl</a> <font color="Maroon" title="c3">R</font></span>)</span> as   <a href="msualg_6.html#V3" title="MSUALG_6:attr.3">invariant</a>   <a href="msualg_6.html#V4" title="MSUALG_6:attr.4">stable</a>  <a href="msualg_4.html#NM4" title="MSUALG_4:NM.4">ManySortedRelation</a> of <font color="Maroon" title="c2">A</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="msualg_6.html#T30" target="_self" title="MSUALG_6:th.30">Th30</a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c4">Q</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">R</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c4">Q</font> &amp; ( for <font color="Olive" title="b1">Q</font> being  <a href="msualg_6.html#V3" title="MSUALG_6:attr.3">invariant</a>   <a href="msualg_6.html#V4" title="MSUALG_6:attr.4">stable</a>  <a href="msualg_4.html#NM4" title="MSUALG_4:NM.4">ManySortedRelation</a> of <font color="Maroon" title="c2">A</font>  st <font color="Maroon" title="c3">R</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Olive" title="b1">Q</font> holds <br/><font color="Maroon" title="c4">Q</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Olive" title="b1">Q</font> ) )</span><br/>

<a NAME="E2:57_1_2"/><span class="lab"><font color="Green" title="E40">A5</font></span>: 
 <a href="msualg_6.html#K7" title="MSUALG_6:func.7">StabCl</a> <font color="Maroon" title="c3">R</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a>  <a href="msualg_6.html#K6" title="MSUALG_6:func.6">InvCl</a> <span class="p1">(<span class="default"><a href="msualg_6.html#K7" title="MSUALG_6:func.7">StabCl</a> <font color="Maroon" title="c3">R</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="msualg_6.html#D11" target="_self" title="MSUALG_6:def.11">Def11</a></span>;<br/>
<a NAME="E3:57_1_2"/>
<font color="Maroon" title="c3">R</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a>  <a href="msualg_6.html#K7" title="MSUALG_6:func.7">StabCl</a> <font color="Maroon" title="c3">R</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="msualg_6.html#D12" target="_self" title="MSUALG_6:def.12">Def12</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:57_1_2"/>
<font color="Maroon" title="c3">R</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c4">Q</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:57_1_2"><span class="lab"><font color="Green" title="E40">A5</font></span></a>, <a class="ref" href="pboole.html#T15" title="PBOOLE:th.15">PBOOLE:15</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">Q</font> being  <a href="msualg_6.html#V3" title="MSUALG_6:attr.3">invariant</a>   <a href="msualg_6.html#V4" title="MSUALG_6:attr.4">stable</a>  <a href="msualg_4.html#NM4" title="MSUALG_4:NM.4">ManySortedRelation</a> of <font color="Maroon" title="c2">A</font>  st <font color="Maroon" title="c3">R</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Olive" title="b1">Q</font> holds <br/><font color="Maroon" title="c4">Q</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Olive" title="b1">Q</font></span><br/>

<span class="kw">let </span><font color="Maroon" title="c5">P</font> be   <a href="msualg_6.html#V3" title="MSUALG_6:attr.3">invariant</a>   <a href="msualg_6.html#V4" title="MSUALG_6:attr.4">stable</a>  <a href="msualg_4.html#NM4" title="MSUALG_4:NM.4">ManySortedRelation</a> of <font color="Maroon" title="c2">A</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">R</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c5">P</font> implies <font color="Maroon" title="c4">Q</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c5">P</font> )</span><br/>

<span class="kw">assume </span><a NAME="E5:57_1_2"/>
<font color="Maroon" title="c3">R</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c5">P</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">Q</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c5">P</font></span><br/>

<a NAME="E6:57_1_2"/><span class="kw">then </span>
 <a href="msualg_6.html#K7" title="MSUALG_6:func.7">StabCl</a> <font color="Maroon" title="c3">R</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c5">P</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="msualg_6.html#D12" target="_self" title="MSUALG_6:def.12">Def12</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:57_1_2"/>
<font color="Maroon" title="c4">Q</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c5">P</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="msualg_6.html#D11" target="_self" title="MSUALG_6:def.11">Def11</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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