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<b>deffunc </b><font color="Maroon">H<sub>1</sub></font>(   <a href="fraenkel.html#M2" title="FRAENKEL:mode.2">Element</a> of  <a href="fraenkel.html#K1" title="FRAENKEL:func.1">Funcs</a> <font color="Maroon" title="c1">A</font>,<a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a> ,   <a href="fraenkel.html#M2" title="FRAENKEL:mode.2">Element</a> of  <a href="fraenkel.html#K1" title="FRAENKEL:func.1">Funcs</a> <font color="Maroon" title="c1">A</font>,<a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a> ) <b>-&gt; </b>   <a href="fraenkel.html#M2" title="FRAENKEL:mode.2">Element</a> of  <a href="fraenkel.html#K1" title="FRAENKEL:func.1">Funcs</a> <font color="Maroon" title="c1">A</font>,<a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a>  = <a href="binop_2.html#K29" title="BINOP_2:func.29">multcomplex</a>  <a href="funcsdom.html#K3" title="FUNCSDOM:func.3">.:</a> $1,$2;<br/>
<b>consider </b><font color="Maroon" title="c2">F</font> being   <a href="binop_1.html#NM2" title="BINOP_1:NM.2">BinOp</a> of  <a href="fraenkel.html#K1" title="FRAENKEL:func.1">Funcs</a> <font color="Maroon" title="c1">A</font>,<a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a> <b> such that </b><br/><a NAME="E2:2_1_1"/><i><font color="Green" title="E2">A1</font></i>: 
for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> being   <a href="fraenkel.html#M2" title="FRAENKEL:mode.2">Element</a> of  <a href="fraenkel.html#K1" title="FRAENKEL:func.1">Funcs</a> <font color="Maroon" title="c1">A</font>,<a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a>  holds  <font color="Maroon" title="c2">F</font> <a href="funcsdom.html#K1" title="FUNCSDOM:func.1">.</a> <font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</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="c2">F</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">f</font>, <font color="Olive" title="b2">g</font> being   <a href="fraenkel.html#M2" title="FRAENKEL:mode.2">Element</a> of  <a href="fraenkel.html#K1" title="FRAENKEL:func.1">Funcs</a> <font color="Maroon" title="c1">A</font>,<a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a>  holds  <font color="Maroon" title="c2">F</font> <a href="funcsdom.html#K1" title="FUNCSDOM:func.1">.</a> <font color="Olive" title="b1">f</font>,<font color="Olive" title="b2">g</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <a href="binop_2.html#K29" title="BINOP_2:func.29">multcomplex</a>  <a href="funcsdom.html#K3" title="FUNCSDOM:func.3">.:</a> <font color="Olive" title="b1">f</font>,<font color="Olive" title="b2">g</font></span><br/>

<b>let </b><font color="Maroon" title="c3">f</font>, <font color="Maroon" title="c4">g</font> be    <a href="fraenkel.html#M2" title="FRAENKEL:mode.2">Element</a> of  <a href="fraenkel.html#K1" title="FRAENKEL:func.1">Funcs</a> <font color="Maroon" title="c1">A</font>,<a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">F</font> <a href="funcsdom.html#K1" title="FUNCSDOM:func.1">.</a> <font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c4">g</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <a href="binop_2.html#K29" title="BINOP_2:func.29">multcomplex</a>  <a href="funcsdom.html#K3" title="FUNCSDOM:func.3">.:</a> <font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c4">g</font></span><br/>



<b>thus </b><a NAME="E3:2_1_1"/>
<font color="Maroon" title="c2">F</font> <a href="funcsdom.html#K1" title="FUNCSDOM:func.1">.</a> <font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c4">g</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <a href="binop_2.html#K29" title="BINOP_2:func.29">multcomplex</a>  <a href="funcsdom.html#K3" title="FUNCSDOM:func.3">.:</a> <font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c4">g</font>
 <b>by </b><i><a class="txt" href="#E2:2_1_1"><i><font color="Green" title="E2">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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