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<b>deffunc </b><font color="Maroon">H<sub>5</sub></font>(   <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c8">D</font> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a> ,   <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c8">D</font> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a> ) <b>-&gt; </b>   <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c8">D</font> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a>  = $1 <a href="lang1.html#K1" title="LANG1:func.1">^</a> $2;<br/>
<b>consider </b><font color="Maroon" title="c10">g</font> being   <a href="binop_1.html#NM2" title="BINOP_1:NM.2">BinOp</a> of <font color="Maroon" title="c8">D</font> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a> <b> such that </b><br/><a NAME="E2:53_1_1"/><i><font color="Green" title="E35">A1</font></i>: 
for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c8">D</font> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a>  holds  <font color="Maroon" title="c10">g</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>5</sub></font>(<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>)
 <b>from </b><i><a class="ref" href="binop_1.html#S4" title="BINOP_1:sch.4">BINOP_1:sch 4</a>();<br/></i>
<b>take </b>
<font color="Maroon" title="c10">g</font> <a href="finsop_1.html#K2" title="FINSOP_1:func.2">"**"</a> <font color="Maroon" title="c9">F</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <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="c8">D</font> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a>  st <br/>( ( for <font color="Olive" title="b2">p</font>, <font color="Olive" title="b3">q</font> being   <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c8">D</font> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a>  holds  <font color="Olive" title="b1">g</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Olive" title="b2">p</font>,<font color="Olive" title="b3">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">p</font> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <font color="Olive" title="b3">q</font> ) &amp; <font color="Maroon" title="c10">g</font> <a href="finsop_1.html#K2" title="FINSOP_1:func.2">"**"</a> <font color="Maroon" title="c9">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">g</font> <a href="finsop_1.html#K2" title="FINSOP_1:func.2">"**"</a> <font color="Maroon" title="c9">F</font> )</span><br/>

<b>take </b>
<font color="Maroon" title="c10">g</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( ( for <font color="Olive" title="b1">p</font>, <font color="Olive" title="b2">q</font> being   <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c8">D</font> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a>  holds  <font color="Maroon" title="c10">g</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Olive" title="b1">p</font>,<font color="Olive" title="b2">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">p</font> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <font color="Olive" title="b2">q</font> ) &amp; <font color="Maroon" title="c10">g</font> <a href="finsop_1.html#K2" title="FINSOP_1:func.2">"**"</a> <font color="Maroon" title="c9">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">g</font> <a href="finsop_1.html#K2" title="FINSOP_1:func.2">"**"</a> <font color="Maroon" title="c9">F</font> )</span><br/>

<b>thus </b><a NAME="E3:53_1_1"/>
( ( for <font color="Olive" title="b1">p</font>, <font color="Olive" title="b2">q</font> being   <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c8">D</font> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a>  holds  <font color="Maroon" title="c10">g</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Olive" title="b1">p</font>,<font color="Olive" title="b2">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">p</font> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <font color="Olive" title="b2">q</font> ) &amp; <font color="Maroon" title="c10">g</font> <a href="finsop_1.html#K2" title="FINSOP_1:func.2">"**"</a> <font color="Maroon" title="c9">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">g</font> <a href="finsop_1.html#K2" title="FINSOP_1:func.2">"**"</a> <font color="Maroon" title="c9">F</font> )
 <b>by </b><i><a class="txt" href="#E2:53_1_1"><i><font color="Green" title="E35">A1</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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