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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E57">Th54</font></span>: <a NAME="T75"><span class="comment"><font color="firebrick">:: MSAFREE5:75</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">s</font> being   <a href="msualg_1.html#NM1" title="MSUALG_1:NM.1">SortSymbol</a> of <font color="Olive" title="b1">S</font><br/>  for <font color="Olive" title="b3">o</font> being   <a href="msualg_1.html#NM2" title="MSUALG_1:NM.2">OperSymbol</a> of <font color="Olive" title="b1">S</font><br/>  for <font color="Olive" title="b4">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="b5">x</font> being    <a href="msafree4.html#M1" title="MSAFREE4:mode.1">Element</a> of <font color="Olive" title="b4">X</font> <a href="msafree4.html#K1" title="MSAFREE4:func.1">.</a> <font color="Olive" title="b2">s</font><br/>  for <font color="Olive" title="b6">p</font> being    <a href="msafree4.html#M1" title="MSAFREE4:mode.1">Element</a> of  <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> (<font color="Olive" title="b3">o</font>,<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="b4">X</font>)</span>)</span>) holds <br/> ( (  for <font color="Olive" title="b7">i</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b7">i</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Olive" title="b6">p</font> holds <br/><font color="Olive" title="b6">p</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Olive" title="b7">i</font> is <font color="Olive" title="b5">x</font> <a href="msafree5.html#V9" title="MSAFREE5:attr.9">-omitting</a>  ) iff <font color="Olive" title="b3">o</font> <a href="msafree5.html#K7" title="MSAFREE5:func.7">-term</a> <font color="Olive" title="b6">p</font> is <font color="Olive" title="b5">x</font> <a href="msafree5.html#V9" title="MSAFREE5:attr.9">-omitting</a>  )</div></div>
