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<span class="kw">let </span><font color="Maroon" title="c1">D</font> be  non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">d</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">D</font><br/> for <font color="Olive" title="b2">g</font> being  <a href="binop_1.html#NM2" title="BINOP_1:NM.2">BinOp</a> of <font color="Maroon" title="c1">D</font> holds  <font color="Olive" title="b2">g</font> <a href="finsop_1.html#K2" title="FINSOP_1:func.2">"**"</a> <span class="p1">(<span class="default">2 <a href="finsop_1.html#K1" title="FINSOP_1:func.1">|-&gt;</a> <font color="Olive" title="b1">d</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">g</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Olive" title="b1">d</font>,<font color="Olive" title="b1">d</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">d</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">D</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">g</font> being  <a href="binop_1.html#NM2" title="BINOP_1:NM.2">BinOp</a> of <font color="Maroon" title="c1">D</font> holds  <font color="Olive" title="b1">g</font> <a href="finsop_1.html#K2" title="FINSOP_1:func.2">"**"</a> <span class="p1">(<span class="default">2 <a href="finsop_1.html#K1" title="FINSOP_1:func.1">|-&gt;</a> <font color="Maroon" title="c2">d</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">g</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c2">d</font>,<font color="Maroon" title="c2">d</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">g</font> be   <a href="binop_1.html#NM2" title="BINOP_1:NM.2">BinOp</a> of <font color="Maroon" title="c1">D</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">g</font> <a href="finsop_1.html#K2" title="FINSOP_1:func.2">"**"</a> <span class="p1">(<span class="default">2 <a href="finsop_1.html#K1" title="FINSOP_1:func.1">|-&gt;</a> <font color="Maroon" title="c2">d</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">g</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c2">d</font>,<font color="Maroon" title="c2">d</font></span><br/>





<span class="kw">thus </span><font color="Maroon" title="c3">g</font> <a href="finsop_1.html#K2" title="FINSOP_1:func.2">"**"</a> <span class="p1">(<span class="default">2 <a href="finsop_1.html#K1" title="FINSOP_1:func.1">|-&gt;</a> <font color="Maroon" title="c2">d</font></span>)</span> = 
<font color="Maroon" title="c3">g</font> <a href="finsop_1.html#K2" title="FINSOP_1:func.2">"**"</a> <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Maroon" title="c2">d</font>,<font color="Maroon" title="c2">d</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_2.html#T75" title="FINSEQ_2:th.75">FINSEQ_2:75</a></span>
<br/>.= 
<font color="Maroon" title="c3">g</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c2">d</font>,<font color="Maroon" title="c2">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="finsop_1.html#T13" target="_self" title="FINSOP_1:th.13">Th13</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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