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<b>let </b><font color="Maroon" title="c1">S</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> non <a href="struct_0.html#V11" title="STRUCT_0:attr.11">void</a>  <a href="msualg_1.html#L1" title="MSUALG_1:struct.1">ManySortedSign</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">A</font> being <a href="msualg_1.html#V4" title="MSUALG_1:attr.4">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/> for <font color="Olive" title="b2">R</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="Olive" title="b1">A</font> holds   <a href="msualg_6.html#K8" title="MSUALG_6:func.8">TRS</a> <font color="Olive" title="b2">R</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Olive" title="b2">R</font></span><br/><b>let </b><font color="Maroon" title="c2">A</font> be  <a href="msualg_1.html#V4" title="MSUALG_1:attr.4">non-empty</a>  <a href="msualg_1.html#L3" title="MSUALG_1:struct.3">MSAlgebra</a> of <font color="Maroon" title="c1">S</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">R</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> holds   <a href="msualg_6.html#K8" title="MSUALG_6:func.8">TRS</a> <font color="Olive" title="b1">R</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Olive" title="b1">R</font></span><br/><b>let </b><font color="Maroon" title="c3">R</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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="msualg_6.html#K8" title="MSUALG_6:func.8">TRS</a> <font color="Maroon" title="c3">R</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Maroon" title="c3">R</font></span><br/>





<b>thus </b><a NAME="E1:61"/>
(  <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> <font color="Maroon" title="c3">R</font> &amp; <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> )
 <b>by </b><i><a class="ref" href="msualg_6.html#D13" target="_self" title="MSUALG_6:def.13">Def13</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> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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