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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E6">Th7</font></span>: <a NAME="T7"><span class="comment"><font color="firebrick">:: PRALG_3:7</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">I</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</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">A</font> being    <a href="pralg_2.html#M1" title="PRALG_2:mode.1">MSAlgebra-Family</a> of <font color="Olive" title="b1">I</font>,<font color="Olive" title="b2">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="b2">S</font>  st  <a href="msualg_1.html#K1" title="MSUALG_1:func.1">the_arity_of</a> <font color="Olive" title="b4">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  holds <br/><span class="p1">(<span class="default"><a href="funct_6.html#K9" title="FUNCT_6:func.9">commute</a> <span class="p2">(<span class="default"><a href="pralg_2.html#K11" title="PRALG_2:func.11">OPER</a> <font color="Olive" title="b3">A</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b4">o</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="funct_2.html#K1" title="FUNCT_2:func.1">Funcs</a> (<font color="Olive" title="b1">I</font>,<span class="p1">(<span class="default"><a href="funct_2.html#K1" title="FUNCT_2:func.1">Funcs</a> (<span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>,<span class="p2">(<span class="default"><a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p3"> { <span class="default"> <span class="p4">(<span class="default"><a href="msualg_1.html#K4" title="MSUALG_1:func.4">Result</a> (<font color="Olive" title="b4">o</font>,<span class="p5">(<span class="default"><font color="Olive" title="b3">A</font> <a href="pralg_2.html#K5" title="PRALG_2:func.5">.</a> <font color="Olive" title="b5">i9</font></span>)</span>)</span>)</span> where <font color="Olive" title="b5">i9</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Olive" title="b1">I</font> : verum </span> } </span> </span>)</span>)</span>)</span>)</div></div>
