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<b>deffunc </b><font color="Maroon">H<sub>3</sub></font>(   <a href="fraenkel.html#M2">Element</a> of  <a href="fraenkel.html#K1">Funcs</a> <font color="Maroon">A</font>,<font color="Maroon">D1</font>,   <a href="fraenkel.html#M2">Element</a> of  <a href="fraenkel.html#K1">Funcs</a> <font color="Maroon">A</font>,<font color="Maroon">D2</font>) <b>-&gt; </b>   <a href="fraenkel.html#M2">Element</a> of  <a href="fraenkel.html#K1">Funcs</a> <font color="Maroon">A</font>,<font color="Maroon">D</font> = <font color="Maroon">f</font> <a href="monoid_1.html#K3" target="_self">.:</a> <font color="Maroon">a<sub>1</sub></font>,<font color="Maroon">a<sub>2</sub></font>;<br/>
<b>consider </b><font color="Maroon">b</font> being   <a href="monoid_1.html#NM1">Function</a> of <span class="p1">(<span class="default"><a href="fraenkel.html#K1">Funcs</a> <font color="Maroon">A</font>,<font color="Maroon">D1</font></span>)</span>,<span class="p1">(<span class="default"><a href="fraenkel.html#K1">Funcs</a> <font color="Maroon">A</font>,<font color="Maroon">D2</font></span>)</span>, <a href="fraenkel.html#K1">Funcs</a> <font color="Maroon">A</font>,<font color="Maroon">D</font><b> such that </b><br/><a NAME="E2:12_1_1"/><i><font color="Green">E43</font></i>: 
for <font color="Olive">f1</font> being   <a href="fraenkel.html#M2">Element</a> of  <a href="fraenkel.html#K1">Funcs</a> <font color="Maroon">A</font>,<font color="Maroon">D1</font><br/> for <font color="Olive">f2</font> being   <a href="fraenkel.html#M2">Element</a> of  <a href="fraenkel.html#K1">Funcs</a> <font color="Maroon">A</font>,<font color="Maroon">D2</font> holds  <font color="Maroon">b</font> <a href="binop_1.html#K2">.</a> <font color="Olive">f1</font>,<font color="Olive">f2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>3</sub></font>(<font color="Olive">f1</font>,<font color="Olive">f2</font>)
 <b>from </b><i><a class="ref" href="binop_1.html#S4">BINOP_1:sch 4</a>();<br/></i>
<b>take </b>
<font color="Maroon">b</font>
;<br/>

<b>let </b><font color="Maroon">f1</font> be    <a href="fraenkel.html#M2">Element</a> of  <a href="fraenkel.html#K1">Funcs</a> <font color="Maroon">A</font>,<font color="Maroon">D1</font>;<br/><b>let </b><font color="Maroon">f2</font> be    <a href="fraenkel.html#M2">Element</a> of  <a href="fraenkel.html#K1">Funcs</a> <font color="Maroon">A</font>,<font color="Maroon">D2</font>;<br/>



<b>thus </b><a NAME="E3:12_1_1"/>
<font color="Maroon">b</font> <a href="binop_1.html#K2">.</a> <font color="Maroon">f1</font>,<font color="Maroon">f2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="monoid_1.html#K3" target="_self">.:</a> <font color="Maroon">f1</font>,<font color="Maroon">f2</font>
 <b>by </b><i/>;<br/>


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