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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="msualg_1.html#V2" title="MSUALG_1:attr.2">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#V5" title="MSUALG_1:attr.5">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">C1</font>, <font color="Olive" title="b3">C2</font> being  <a href="msualg_4.html#NM5" title="MSUALG_4:NM.5">MSCongruence</a> of <font color="Olive" title="b1">A</font> holds  <font color="Olive" title="b2">C1</font> <a href="msualg_5.html#K4" title="MSUALG_5:func.4">"\/"</a> <font color="Olive" title="b3">C2</font> is   <a href="msualg_4.html#NM5" title="MSUALG_4:NM.5">MSCongruence</a> of <font color="Olive" title="b1">A</font></span><br/><b>let </b><font color="Maroon" title="c2">A</font> be  <a href="msualg_1.html#V5" title="MSUALG_1:attr.5">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">C1</font>, <font color="Olive" title="b2">C2</font> being  <a href="msualg_4.html#NM5" title="MSUALG_4:NM.5">MSCongruence</a> of <font color="Maroon" title="c2">A</font> holds  <font color="Olive" title="b1">C1</font> <a href="msualg_5.html#K4" title="MSUALG_5:func.4">"\/"</a> <font color="Olive" title="b2">C2</font> is   <a href="msualg_4.html#NM5" title="MSUALG_4:NM.5">MSCongruence</a> of <font color="Maroon" title="c2">A</font></span><br/><b>let </b><font color="Maroon" title="c3">C1</font>, <font color="Maroon" title="c4">C2</font> be   <a href="msualg_4.html#NM5" title="MSUALG_4:NM.5">MSCongruence</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"> <font color="Maroon" title="c3">C1</font> <a href="msualg_5.html#K4" title="MSUALG_5:func.4">"\/"</a> <font color="Maroon" title="c4">C2</font> is   <a href="msualg_4.html#NM5" title="MSUALG_4:NM.5">MSCongruence</a> of <font color="Maroon" title="c2">A</font></span><br/>





<b>reconsider </b><font color="Maroon" title="c5">C</font> = <font color="Maroon" title="c3">C1</font> <a href="msualg_5.html#K4" title="MSUALG_5:func.4">"\/"</a> <font color="Maroon" title="c4">C2</font> as  <a href="msualg_4.html#V2" title="MSUALG_4:attr.2">MSEquivalence_Relation-like</a> <a href="msualg_4.html#NM3" title="MSUALG_4:NM.3">ManySortedRelation</a> of the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c2">A</font> ;<br/>
<b>reconsider </b><font color="Maroon" title="c6">C</font> = <font color="Maroon" title="c5">C</font> as   <a href="msualg_4.html#NM4" title="MSUALG_4:NM.4">ManySortedRelation</a> of <font color="Maroon" title="c2">A</font> ;<br/>
<b>reconsider </b><font color="Maroon" title="c7">C</font> = <font color="Maroon" title="c6">C</font> as  <a href="msualg_4.html#V3" title="MSUALG_4:attr.3">MSEquivalence-like</a> <a href="msualg_4.html#NM4" title="MSUALG_4:NM.4">ManySortedRelation</a> of <font color="Maroon" title="c2">A</font> <b>by </b><i><a class="ref" href="msualg_4.html#D5" title="MSUALG_4:def.5">MSUALG_4:def 5</a></i>;<br/>
<a NAME="E4:23"/>
for <font color="Olive" title="b1">o</font> being  <a href="msualg_1.html#NM2" title="MSUALG_1:NM.2">OperSymbol</a> of <font color="Maroon" title="c1">S</font><br/> for <font color="Olive" title="b2">x</font>, <font color="Olive" title="b3">y</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> <font color="Olive" title="b1">o</font>,<font color="Maroon" title="c2">A</font>  st ( for <font color="Olive" title="b4">n</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Olive" title="b4">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Olive" title="b2">x</font> holds <br/><span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b2">x</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b4">n</font></span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b3">y</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b4">n</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">C</font> <a href="msualg_4.html#K2" title="MSUALG_4:func.2">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msualg_1.html#K1" title="MSUALG_1:func.1">the_arity_of</a> <font color="Olive" title="b1">o</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Olive" title="b4">n</font></span>)</span> ) holds <br/><span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="msualg_1.html#K5" title="MSUALG_1:func.5">Den</a> <font color="Olive" title="b1">o</font>,<font color="Maroon" title="c2">A</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">x</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="msualg_1.html#K5" title="MSUALG_1:func.5">Den</a> <font color="Olive" title="b1">o</font>,<font color="Maroon" title="c2">A</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b3">y</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">C</font> <a href="msualg_4.html#K2" title="MSUALG_4:func.2">.</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K2" title="MSUALG_1:func.2">the_result_sort_of</a> <font color="Olive" title="b1">o</font></span>)</span>
 
<b>by </b><i><a class="ref" href="msualg_5.html#T16" target="_self" title="MSUALG_5:th.16">Th16</a></i>;<br/>
<b>hence </b><a NAME="E5:23"/>
<font color="Maroon" title="c3">C1</font> <a href="msualg_5.html#K4" title="MSUALG_5:func.4">"\/"</a> <font color="Maroon" title="c4">C2</font> is   <a href="msualg_4.html#NM5" title="MSUALG_4:NM.5">MSCongruence</a> of <font color="Maroon" title="c2">A</font>
 <b>by </b><i><a class="ref" href="msualg_4.html#D6" title="MSUALG_4:def.6">MSUALG_4:def 6</a></i>; <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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