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<div><span class="kw">theorem </span><a NAME="T27"><span class="comment"><font color="firebrick">:: SETWOP_2:27</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">D</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">d</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Olive" title="b1">D</font><br/>  for <font color="Olive" title="b3">F</font> being   <a href="binop_1.html#NM2" title="BINOP_1:NM.2">BinOp</a> of <font color="Olive" title="b1">D</font><br/>  for <font color="Olive" title="b4">i</font>, <font color="Olive" title="b5">j</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b3">F</font> is  <a href="binop_1.html#V1" title="BINOP_1:attr.1">commutative</a>  &amp; <font color="Olive" title="b3">F</font> is  <a href="binop_1.html#V2" title="BINOP_1:attr.2">associative</a>  &amp; ( ( <font color="Olive" title="b4">i</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1 &amp; <font color="Olive" title="b5">j</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1 ) or <font color="Olive" title="b3">F</font> is  <a href="setwiseo.html#V1" title="SETWISEO:attr.1">having_a_unity</a>  ) holds <br/><font color="Olive" title="b3">F</font> <a href="finsop_1.html#K1" title="FINSOP_1:func.1">"**"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b4">i</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Olive" title="b5">j</font></span>)</span> <a href="finseq_2.html#K5" title="FINSEQ_2:func.5">|-&gt;</a> <font color="Olive" title="b2">d</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">F</font> <a href="finsop_1.html#K1" title="FINSOP_1:func.1">"**"</a> <span class="p1">(<span class="default"><font color="Olive" title="b5">j</font> <a href="finseq_2.html#K5" title="FINSEQ_2:func.5">|-&gt;</a> <span class="p2">(<span class="default"><font color="Olive" title="b3">F</font> <a href="finsop_1.html#K1" title="FINSOP_1:func.1">"**"</a> <span class="p3">(<span class="default"><font color="Olive" title="b4">i</font> <a href="finseq_2.html#K5" title="FINSEQ_2:func.5">|-&gt;</a> <font color="Olive" title="b2">d</font></span>)</span></span>)</span></span>)</span></div></div>
