<?xml version="1.0"?>
<div><span class="kw">theorem </span><a NAME="T41"><span class="comment"><font color="firebrick">:: SETWOP_2:41</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>, <font color="Olive" title="b4">G</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="b5">p</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Olive" title="b1">D</font>  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="b3">F</font> is  <a href="setwiseo.html#V1" title="SETWISEO:attr.1">having_a_unity</a>  &amp; <font color="Olive" title="b3">F</font> is  <a href="finseqop.html#V1" title="FINSEQOP:attr.1">having_an_inverseOp</a>  &amp; <font color="Olive" title="b4">G</font> <a href="binop_1.html#R6" title="BINOP_1:pred.6">is_distributive_wrt</a> <font color="Olive" title="b3">F</font> holds <br/><font color="Olive" title="b4">G</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<span class="p1">(<span class="default"><font color="Olive" title="b3">F</font> <a href="finsop_1.html#K1" title="FINSOP_1:func.1">"**"</a> <font color="Olive" title="b5">p</font></span>)</span>,<font color="Olive" title="b2">d</font>) <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="b4">G</font> <a href="finseqop.html#K2" title="FINSEQOP:func.2">[:]</a> (<font color="Olive" title="b5">p</font>,<font color="Olive" title="b2">d</font>)</span>)</span></div></div>
