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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E41">Th45</font></span>: <a NAME="T50"><span class="comment"><font color="firebrick">:: AOFA_A00:50</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="relat_1.html#V2" title="RELAT_1:attr.2">V2</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">f</font> being    <a href="pboole.html#M2" title="PBOOLE:mode.2">ManySortedFunction</a> of <span class="p1">(<span class="default"><font color="Olive" title="b2">A</font> <a href="finseq_2.html#K6" title="FINSEQ_2:func.6">#</a></span>)</span> <a href="msafree4.html#K3" title="MSAFREE4:func.3">*</a>  the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <font color="Olive" title="b1">S</font>,<font color="Olive" title="b2">A</font> <a href="msafree4.html#K3" title="MSAFREE4:func.3">*</a>  the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <font color="Olive" title="b1">S</font><br/>  for <font color="Olive" title="b4">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="b5">d</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive" title="b2">A</font> <a href="finseq_2.html#K6" title="FINSEQ_2:func.6">#</a></span>)</span> <a href="msafree4.html#K3" title="MSAFREE4:func.3">*</a>  the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <font color="Olive" title="b1">S</font></span>)</span> <a href="msafree4.html#K1" title="MSAFREE4:func.1">.</a> <font color="Olive" title="b4">o</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b2">A</font> <a href="msafree4.html#K3" title="MSAFREE4:func.3">*</a>  the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <font color="Olive" title="b1">S</font></span>)</span> <a href="msafree4.html#K1" title="MSAFREE4:func.1">.</a> <font color="Olive" title="b4">o</font></span>)</span> holds  <font color="Olive" title="b3">f</font> <a href="aofa_a00.html#K1" title="AOFA_A00:func.1">+*</a> (<font color="Olive" title="b4">o</font>,<font color="Olive" title="b5">d</font>) is    <a href="pboole.html#M2" title="PBOOLE:mode.2">ManySortedFunction</a> of <span class="p1">(<span class="default"><font color="Olive" title="b2">A</font> <a href="finseq_2.html#K6" title="FINSEQ_2:func.6">#</a></span>)</span> <a href="msafree4.html#K3" title="MSAFREE4:func.3">*</a>  the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <font color="Olive" title="b1">S</font>,<font color="Olive" title="b2">A</font> <a href="msafree4.html#K3" title="MSAFREE4:func.3">*</a>  the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <font color="Olive" title="b1">S</font></div></div>
