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<div><span class="kw">theorem </span><a NAME="T32"><span class="comment"><font color="firebrick">:: MSUALG_9:32</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">S</font> being   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> <br/>  for <font color="Olive" title="b2">A</font> being    <a href="msualg_1.html#L3" title="MSUALG_1:struct.3">MSAlgebra</a> over <font color="Olive" title="b1">S</font><br/>  for <font color="Olive" title="b3">C1</font>, <font color="Olive" title="b4">C2</font> being   <a href="msualg_4.html#V2" title="MSUALG_4:attr.2">MSEquivalence-like</a>  <a href="msualg_4.html#NM3" title="MSUALG_4:NM.3">ManySortedRelation</a> of <font color="Olive" title="b2">A</font>  st <font color="Olive" title="b3">C1</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Olive" title="b4">C2</font> holds <br/> for <font color="Olive" title="b5">i</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">S</font><br/>  for <font color="Olive" title="b6">x</font>, <font color="Olive" title="b7">y</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Olive" title="b2">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b5">i</font>  st <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b6">x</font>,<font color="Olive" title="b7">y</font></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="Olive" title="b3">C1</font> <a href="msualg_4.html#K2" title="MSUALG_4:func.2">.</a> <font color="Olive" title="b5">i</font> holds <br/>(  <a href="msualg_4.html#K3" title="MSUALG_4:func.3">Class</a> (<font color="Olive" title="b3">C1</font>,<font color="Olive" title="b6">x</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="msualg_4.html#K3" title="MSUALG_4:func.3">Class</a> (<font color="Olive" title="b4">C2</font>,<font color="Olive" title="b7">y</font>) &amp; ( <font color="Olive" title="b2">A</font> is  <a href="msualg_1.html#V4" title="MSUALG_1:attr.4">non-empty</a>  implies  <a href="msualg_4.html#K3" title="MSUALG_4:func.3">Class</a> (<font color="Olive" title="b3">C1</font>,<font color="Olive" title="b7">y</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="msualg_4.html#K3" title="MSUALG_4:func.3">Class</a> (<font color="Olive" title="b4">C2</font>,<font color="Olive" title="b6">x</font>) ) )</div></div>
