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<span class="kw">let </span><font color="Maroon" title="c1">c</font> be   <a href="xcmplx_0.html#V1" title="XCMPLX_0:attr.1">complex</a>   <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">f</font> being  <a href="valued_0.html#V1" title="VALUED_0:attr.1">complex-valued</a>  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a> holds  <span class="p1">(<span class="default"><font color="Olive" title="b1">f</font> <a href="valued_2.html#K14" title="VALUED_2:func.14">(/)</a> <font color="Maroon" title="c1">c</font></span>)</span> <a href="valued_1.html#K39" title="VALUED_1:func.39">^2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">f</font> <a href="valued_1.html#K39" title="VALUED_1:func.39">^2</a> </span>)</span> <a href="valued_2.html#K14" title="VALUED_2:func.14">(/)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">c</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">f</font> be   <a href="valued_0.html#V1" title="VALUED_0:attr.1">complex-valued</a>  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="valued_2.html#K14" title="VALUED_2:func.14">(/)</a> <font color="Maroon" title="c1">c</font></span>)</span> <a href="valued_1.html#K39" title="VALUED_1:func.39">^2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="valued_1.html#K39" title="VALUED_1:func.39">^2</a> </span>)</span> <a href="valued_2.html#K14" title="VALUED_2:func.14">(/)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">c</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span></span><br/>



<span class="kw">thus </span> <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="valued_2.html#K14" title="VALUED_2:func.14">(/)</a> <font color="Maroon" title="c1">c</font></span>)</span> <a href="valued_1.html#K39" title="VALUED_1:func.39">^2</a> </span>)</span> = 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="valued_2.html#K14" title="VALUED_2:func.14">(/)</a> <font color="Maroon" title="c1">c</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="valued_1.html#T11" title="VALUED_1:th.11">VALUED_1:11</a></span>
<br/>.= 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c2">f</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="valued_2.html#T28" title="VALUED_2:th.28">VALUED_2:28</a></span>
<br/>.= 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="valued_1.html#K39" title="VALUED_1:func.39">^2</a> </span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="valued_1.html#T11" title="VALUED_1:th.11">VALUED_1:11</a></span>
<br/>.= 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="valued_1.html#K39" title="VALUED_1:func.39">^2</a> </span>)</span> <a href="valued_2.html#K14" title="VALUED_2:func.14">(/)</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">c</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="valued_2.html#T28" title="VALUED_2:th.28">VALUED_2:28</a></span>
; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="funct_1.html#D17" title="FUNCT_1:def.17">FUNCT_1:def 17</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   holds <br/>(  not <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">proj1</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="valued_2.html#K14" title="VALUED_2:func.14">(/)</a> <font color="Maroon" title="c1">c</font></span>)</span> <a href="valued_1.html#K39" title="VALUED_1:func.39">^2</a> </span>)</span> or <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="valued_2.html#K14" title="VALUED_2:func.14">(/)</a> <font color="Maroon" title="c1">c</font></span>)</span> <a href="valued_1.html#K39" title="VALUED_1:func.39">^2</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="valued_1.html#K39" title="VALUED_1:func.39">^2</a> </span>)</span> <a href="valued_2.html#K14" title="VALUED_2:func.14">(/)</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">c</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> )</span><br/>

<span class="kw">let </span><font color="Maroon" title="c3">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">proj1</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="valued_2.html#K14" title="VALUED_2:func.14">(/)</a> <font color="Maroon" title="c1">c</font></span>)</span> <a href="valued_1.html#K39" title="VALUED_1:func.39">^2</a> </span>)</span> or <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="valued_2.html#K14" title="VALUED_2:func.14">(/)</a> <font color="Maroon" title="c1">c</font></span>)</span> <a href="valued_1.html#K39" title="VALUED_1:func.39">^2</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="valued_1.html#K39" title="VALUED_1:func.39">^2</a> </span>)</span> <a href="valued_2.html#K14" title="VALUED_2:func.14">(/)</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">c</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">x</font> )</span><br/>

<span class="kw">assume </span><a NAME="E2:16"/>
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="valued_2.html#K14" title="VALUED_2:func.14">(/)</a> <font color="Maroon" title="c1">c</font></span>)</span> <a href="valued_1.html#K39" title="VALUED_1:func.39">^2</a> </span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="valued_2.html#K14" title="VALUED_2:func.14">(/)</a> <font color="Maroon" title="c1">c</font></span>)</span> <a href="valued_1.html#K39" title="VALUED_1:func.39">^2</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="valued_1.html#K39" title="VALUED_1:func.39">^2</a> </span>)</span> <a href="valued_2.html#K14" title="VALUED_2:func.14">(/)</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">c</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">x</font></span><br/>

<span class="kw">thus </span><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="valued_2.html#K14" title="VALUED_2:func.14">(/)</a> <font color="Maroon" title="c1">c</font></span>)</span> <a href="valued_1.html#K39" title="VALUED_1:func.39">^2</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">x</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="valued_2.html#K14" title="VALUED_2:func.14">(/)</a> <font color="Maroon" title="c1">c</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">x</font></span>)</span> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> 
<span class="kw">by</span> <span class="lab"><a class="ref" href="valued_1.html#T11" title="VALUED_1:th.11">VALUED_1:11</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">x</font></span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <font color="Maroon" title="c1">c</font></span>)</span> <a href="square_1.html#K4" title="SQUARE_1:func.4">^2</a> 
<span class="kw">by</span> <span class="lab"><a class="ref" href="valued_2.html#T29" title="VALUED_2:th.29">VALUED_2:29</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">x</font></span>)</span> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">c</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="xcmplx_1.html#T77" title="XCMPLX_1:th.77">XCMPLX_1:77</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="valued_1.html#K39" title="VALUED_1:func.39">^2</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">x</font></span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">c</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="valued_1.html#T11" title="VALUED_1:th.11">VALUED_1:11</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="valued_1.html#K39" title="VALUED_1:func.39">^2</a> </span>)</span> <a href="valued_2.html#K14" title="VALUED_2:func.14">(/)</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">c</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">x</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="valued_2.html#T29" title="VALUED_2:th.29">VALUED_2:29</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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