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<div>:: <span class="kw">deftheorem </span>   defines <a href="pralg_1.html#K21" title="PRALG_1:func.21">ProdOp</a> <a onclick="hs(this)" href="javascript:()">PRALG_1:def 23 : <br/></a><span> for <font color="Olive" title="b1">J</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">A</font> being   <a href="pralg_1.html#V1" title="PRALG_1:attr.1">Univ_Alg-yielding</a>   <a href="pralg_1.html#V3" title="PRALG_1:attr.3">equal-signature</a>  <a href="pboole.html#NM1" title="PBOOLE:NM.1">ManySortedSet</a> of <font color="Olive" title="b1">J</font><br/>  for <font color="Olive" title="b3">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b3">n</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> <span class="p1">(<span class="default"><a href="pralg_1.html#K15" title="PRALG_1:func.15">ComSign</a> <font color="Olive" title="b2">A</font></span>)</span> holds <br/> for <font color="Olive">b<sub>4</sub></font> being   <a href="pralg_1.html#V4" title="PRALG_1:attr.4">equal-arity</a>   <a href="pralg_1.html#M1" title="PRALG_1:mode.1">ManySortedOperation</a> of  <a href="pralg_1.html#K14" title="PRALG_1:func.14">Carrier</a> <font color="Olive" title="b2">A</font> holds <br/> ( <font color="Olive">b<sub>4</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pralg_1.html#K21" title="PRALG_1:func.21">ProdOp</a> (<font color="Olive" title="b2">A</font>,<font color="Olive" title="b3">n</font>) iff  for <font color="Olive" title="b5">j</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Olive" title="b1">J</font><br/>  for <font color="Olive" title="b6">o</font> being   <a href="unialg_2.html#NM3" title="UNIALG_2:NM.3">operation</a> of <span class="p1">(<span class="default"><font color="Olive" title="b2">A</font> <a href="pralg_1.html#K12" title="PRALG_1:func.12">.</a> <font color="Olive" title="b5">j</font></span>)</span>  st  the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <span class="p1">(<span class="default"><font color="Olive" title="b2">A</font> <a href="pralg_1.html#K12" title="PRALG_1:func.12">.</a> <font color="Olive" title="b5">j</font></span>)</span> <a href="partfun1.html#K8" title="PARTFUN1:func.8">.</a> <font color="Olive" title="b3">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b6">o</font> holds <br/><font color="Olive">b<sub>4</sub></font> <a href="pralg_1.html#K16" title="PRALG_1:func.16">.</a> <font color="Olive" title="b5">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b6">o</font> );<br/></span></div>
