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<span class="kw">deffunc </span><font color="Maroon">H<sub>1</sub></font>(  <a href="xcmplx_0.html#NM1" title="XCMPLX_0:NM.1">Complex</a>,   <a href="rfunct_3.html#M2" title="RFUNCT_3:mode.2">Element</a> of  <a href="rfunct_3.html#K3" title="RFUNCT_3:func.3">PFuncs</a> (<font color="Maroon" title="c1">A</font>,<a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a>)) <span class="kw">-&gt; </span>   <a href="rfunct_3.html#M2" title="RFUNCT_3:mode.2">Element</a> of  <a href="rfunct_3.html#K3" title="RFUNCT_3:func.3">PFuncs</a> (<font color="Maroon" title="c1">A</font>,<a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a>) = $1 <a href="lpspacc1.html#K5" title="LPSPACC1:func.5">(#)</a> $2;<br/>
<span class="kw">consider </span><font color="Maroon" title="c2">F</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a>,<span class="p2">(<span class="default"><a href="rfunct_3.html#K3" title="RFUNCT_3:func.3">PFuncs</a> (<font color="Maroon" title="c1">A</font>,<a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a>)</span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<span class="p1">(<span class="default"><a href="rfunct_3.html#K3" title="RFUNCT_3:func.3">PFuncs</a> (<font color="Maroon" title="c1">A</font>,<a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a>)</span>)</span><span class="kw"> such that </span><br/><a NAME="E2:10_1_1"/><span class="lab"><font color="Green" title="E5">A1</font></span>: 
 for <font color="Olive" title="b1">a</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a> <br/>  for <font color="Olive" title="b2">f</font> being    <a href="rfunct_3.html#M2" title="RFUNCT_3:mode.2">Element</a> of  <a href="rfunct_3.html#K3" title="RFUNCT_3:func.3">PFuncs</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="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">f</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">f</font>)
 <span class="kw">from</span> <span class="lab"><a class="ref" href="binop_1.html#S4" onmouseover="rs('binop_1/S4')" onmouseout="rh()">BINOP_1:sch 4</a>();<br/></span>
<span class="kw">take </span>
<font color="Maroon" title="c2">F</font>
; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">a</font> being   <a href="xcmplx_0.html#NM1" title="XCMPLX_0:NM.1">Complex</a><br/>  for <font color="Olive" title="b2">f</font> being    <a href="rfunct_3.html#M2" title="RFUNCT_3:mode.2">Element</a> of  <a href="rfunct_3.html#K3" title="RFUNCT_3:func.3">PFuncs</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="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">f</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="lpspacc1.html#K5" title="LPSPACC1:func.5">(#)</a> <font color="Olive" title="b2">f</font></span><br/>

<span class="kw">let </span><font color="Maroon" title="c3">a</font> be   <a href="xcmplx_0.html#NM1" title="XCMPLX_0:NM.1">Complex</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">f</font> being    <a href="rfunct_3.html#M2" title="RFUNCT_3:mode.2">Element</a> of  <a href="rfunct_3.html#K3" title="RFUNCT_3:func.3">PFuncs</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="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c3">a</font>,<font color="Olive" title="b1">f</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> <a href="lpspacc1.html#K5" title="LPSPACC1:func.5">(#)</a> <font color="Olive" title="b1">f</font></span><br/>

<a NAME="E3:10_1_1"/>
<font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xcmplx_0.html#D2" onmouseover="rs('xcmplx_0/D2')" onmouseout="rh()">XCMPLX_0:def 2</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:10_1_1"/>
 for <font color="Olive" title="b1">f</font> being    <a href="rfunct_3.html#M2" title="RFUNCT_3:mode.2">Element</a> of  <a href="rfunct_3.html#K3" title="RFUNCT_3:func.3">PFuncs</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="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c3">a</font>,<font color="Olive" title="b1">f</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> <a href="lpspacc1.html#K5" title="LPSPACC1:func.5">(#)</a> <font color="Olive" title="b1">f</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:10_1_1"><span class="lab"><font color="Green" title="E5">A1</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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