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<b>let </b><font color="Maroon">X</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">Y</font> be   <a href="clvect_1.html#NM2">ComplexLinearSpace</a>;<br/>



<b>deffunc </b><font color="Maroon">H<sub>1</sub></font>(  <a href="cfunct_1.html#NM1">Complex</a>,   <a href="fraenkel.html#M2">Element</a> of  <a href="fraenkel.html#K1">Funcs</a> <font color="Maroon">X</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">Y</font>) <b>-&gt; </b>   <a href="fraenkel.html#M2">Element</a> of  <a href="fraenkel.html#K1">Funcs</a> <font color="Maroon">X</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">Y</font> =  <a href="funcsdom.html#K3">@</a> <span class="p1">(<span class="default">the <a href="clvect_1.html#U1">Mult</a> of <font color="Maroon">Y</font> <a href="clopban1.html#K1" target="_self">[;]</a> <font color="Maroon">a<sub>1</sub></font>,<font color="Maroon">a<sub>2</sub></font></span>)</span>;<br/>
<b>consider </b><font color="Maroon">F</font> being   <a href="funct_2.html#NM1">Function</a> of <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><a href="numbers.html#K2">COMPLEX</a> ,<span class="p2">(<span class="default"><a href="fraenkel.html#K1">Funcs</a> <font color="Maroon">X</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">Y</font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>, <a href="fraenkel.html#K1">Funcs</a> <font color="Maroon">X</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">Y</font><b> such that </b><br/><a NAME="E2:2"/><i><font color="Green">E38</font></i>: 
for <font color="Olive">c</font> being  <a href="cfunct_1.html#NM1">Complex</a><br/> for <font color="Olive">f</font> being   <a href="fraenkel.html#M2">Element</a> of  <a href="fraenkel.html#K1">Funcs</a> <font color="Maroon">X</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">Y</font> holds  <font color="Maroon">F</font> <a href="binop_1.html#K2">.</a> <font color="Olive">c</font>,<font color="Olive">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">c</font>,<font color="Olive">f</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">F</font>
;<br/>

<b>let </b><font color="Maroon">c</font> be   <a href="cfunct_1.html#NM1">Complex</a>;<br/><b>let </b><font color="Maroon">f</font> be    <a href="fraenkel.html#M2">Element</a> of  <a href="fraenkel.html#K1">Funcs</a> <font color="Maroon">X</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">Y</font>;<br/><b>let </b><font color="Maroon">x</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">X</font>;<br/>





<a NAME="E3:2"/><i><font color="Green">E44</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="funcsdom.html#K2">.</a> <span class="p2"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c</font>,<font color="Maroon">f</font></span><a href="domain_1.html#K1">]</a></span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">X</font>
 
<b>by </b><i><a class="ref" href="funct_2.html#T169">FUNCT_2:169</a></i>;<br/>
<font color="Maroon">F</font> <a href="binop_1.html#K2">.</a> <font color="Maroon">c</font>,<font color="Maroon">f</font> = 
 <a href="funcsdom.html#K3">@</a> <span class="p1">(<span class="default">the <a href="clvect_1.html#U1">Mult</a> of <font color="Maroon">Y</font> <a href="clopban1.html#K1" target="_self">[;]</a> <font color="Maroon">c</font>,<font color="Maroon">f</font></span>)</span>
<b>by </b><i/>
<br/>.= 
the <a href="clvect_1.html#U1">Mult</a> of <font color="Maroon">Y</font> <a href="clopban1.html#K1" target="_self">[;]</a> <font color="Maroon">c</font>,<font color="Maroon">f</font>
<b>by </b><i><a class="ref" href="funcsdom.html#D1">FUNCSDOM:def 1</a></i>
;<br/>
<b>hence </b><span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="funcsdom.html#K2">.</a> <span class="p2"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c</font>,<font color="Maroon">f</font></span><a href="domain_1.html#K1">]</a></span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> = 
the <a href="clvect_1.html#U1">Mult</a> of <font color="Maroon">Y</font> <a href="binop_1.html#K2">.</a> <font color="Maroon">c</font>,<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font></span>)</span>
<b>by </b><i>, <a class="ref" href="funcop_1.html#T42">FUNCOP_1:42</a></i>
<br/>.= 
<font color="Maroon">c</font> <a href="clvect_1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font></span>)</span>
<b>by </b><i><a class="ref" href="clvect_1.html#D1">CLVECT_1:def 1</a></i>
;<br/><br/>


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