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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E125">Th135</font></span>: <a NAME="T144"><span class="comment"><font color="firebrick">:: MSAFREE5:144</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">X</font> being  <a href="relat_1.html#V2" title="RELAT_1:attr.2">V5</a>() <a href="pboole.html#NM1" title="PBOOLE:NM.1">ManySortedSet</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">S</font><br/>  for <font color="Olive" title="b3">t</font> being   <a href="msafree3.html#NM1" title="MSAFREE3:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="msafree3.html#K1" title="MSAFREE3:func.1">Free</a> (<font color="Olive" title="b1">S</font>,<font color="Olive" title="b2">X</font>)</span>)</span><br/>  for <font color="Olive" title="b4">h</font> being    <a href="msualg_6.html#M1" title="MSUALG_6:mode.1">Endomorphism</a> of  <a href="msafree3.html#K1" title="MSAFREE3:func.1">Free</a> (<font color="Olive" title="b1">S</font>,<font color="Olive" title="b2">X</font>) holds <br/> (  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Olive" title="b3">t</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">h</font> <a href="msafree5.html#K4" title="MSAFREE5:func.4">.</a> <font color="Olive" title="b3">t</font></span>)</span> &amp; (  for <font color="Olive" title="b5">I</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <font color="Olive" title="b5">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b6">xi</font> where <font color="Olive" title="b6">xi</font> is    <a href="trees_1.html#M1" title="TREES_1:mode.1">Element</a> of  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Olive" title="b3">t</font> :  ex <font color="Olive" title="b7">s</font> being   <a href="msualg_1.html#NM1" title="MSUALG_1:NM.1">SortSymbol</a> of <font color="Olive" title="b1">S</font> ex <font color="Olive" title="b8">x</font> being    <a href="msafree4.html#M1" title="MSAFREE4:mode.1">Element</a> of <font color="Olive" title="b2">X</font> <a href="msafree4.html#K1" title="MSAFREE4:func.1">.</a> <font color="Olive" title="b7">s</font> st <font color="Olive" title="b3">t</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b6">xi</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Olive" title="b8">x</font>,<font color="Olive" title="b7">s</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> </span> } </span>  holds <br/><font color="Olive" title="b3">t</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Olive" title="b3">t</font></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <font color="Olive" title="b5">I</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">h</font> <a href="msafree5.html#K4" title="MSAFREE5:func.4">.</a> <font color="Olive" title="b3">t</font></span>)</span> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Olive" title="b3">t</font></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <font color="Olive" title="b5">I</font></span>)</span> ) )</div></div>
