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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E25">Th4A</font></span>: <a NAME="T25"><span class="comment"><font color="firebrick">:: MSAFREE5:25</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">i</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b2">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="b3">o</font> being   <a href="msualg_1.html#NM2" title="MSUALG_1:NM.2">OperSymbol</a> of <font color="Olive" title="b2">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="b2">S</font><br/>  for <font color="Olive" title="b5">T</font> being  <font color="Olive">b<sub>4</sub></font>,<font color="Olive">b<sub>2</sub></font> <a href="msafree4.html#V5" title="MSAFREE4:attr.5">-terms</a>   <a href="msafree4.html#V6" title="MSAFREE4:attr.6">all_vars_including</a>   <a href="msafree4.html#V7" title="MSAFREE4:attr.7">inheriting_operations</a>   <a href="msafree4.html#V8" title="MSAFREE4:attr.8">free_in_itself</a>   <a href="msualg_1.html#L3" title="MSUALG_1:struct.3">MSAlgebra</a> over <font color="Olive" title="b2">S</font><br/>  for <font color="Olive" title="b6">q</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>,<font color="Olive" title="b5">T</font>)  st <font color="Olive" title="b1">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">q</font> holds <br/> <a href="msafree5.html#K3" title="MSAFREE5:func.3">the_sort_of</a> <span class="p1">(<span class="default"><font color="Olive" title="b6">q</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Olive" title="b1">i</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K1" title="MSUALG_1:func.1">the_arity_of</a> <font color="Olive" title="b3">o</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Olive" title="b1">i</font></div></div>
