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<span class="kw">let </span><font color="Maroon" title="c1">c1</font>, <font color="Maroon" title="c2">c2</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>, <font color="Olive" title="b2">g</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>  st <font color="Maroon" title="c1">c1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>  &amp; <font color="Maroon" title="c2">c2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>  holds <br/><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">c1</font></span>)</span> <a href="valued_1.html#K45" title="VALUED_1:func.45">-</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">g</font> <a href="valued_2.html#K14" title="VALUED_2:func.14">(/)</a> <font color="Maroon" title="c2">c2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">f</font> <a href="valued_1.html#NK26" title="VALUED_1:NK.26">(#)</a> <font color="Maroon" title="c2">c2</font></span>)</span> <a href="valued_1.html#K45" title="VALUED_1:func.45">-</a> <span class="p2">(<span class="default"><font color="Olive" title="b2">g</font> <a href="valued_1.html#NK26" title="VALUED_1:NK.26">(#)</a> <font color="Maroon" title="c1">c1</font></span>)</span></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">c1</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">c2</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c3">f</font>, <font color="Maroon" title="c4">g</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"> ( <font color="Maroon" title="c1">c1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>  &amp; <font color="Maroon" title="c2">c2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>  implies <span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="valued_2.html#K14" title="VALUED_2:func.14">(/)</a> <font color="Maroon" title="c1">c1</font></span>)</span> <a href="valued_1.html#K45" title="VALUED_1:func.45">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">g</font> <a href="valued_2.html#K14" title="VALUED_2:func.14">(/)</a> <font color="Maroon" title="c2">c2</font></span>)</span> <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="c3">f</font> <a href="valued_1.html#NK26" title="VALUED_1:NK.26">(#)</a> <font color="Maroon" title="c2">c2</font></span>)</span> <a href="valued_1.html#K45" title="VALUED_1:func.45">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">g</font> <a href="valued_1.html#NK26" title="VALUED_1:NK.26">(#)</a> <font color="Maroon" title="c1">c1</font></span>)</span></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">c1</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">c2</font></span>)</span> )</span><br/>







<span class="kw">assume </span><a NAME="E1:12"/><span class="lab"><font color="Green" title="E3">A1</font></span>: 
( <font color="Maroon" title="c1">c1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>  &amp; <font color="Maroon" title="c2">c2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</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="c3">f</font> <a href="valued_2.html#K14" title="VALUED_2:func.14">(/)</a> <font color="Maroon" title="c1">c1</font></span>)</span> <a href="valued_1.html#K45" title="VALUED_1:func.45">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">g</font> <a href="valued_2.html#K14" title="VALUED_2:func.14">(/)</a> <font color="Maroon" title="c2">c2</font></span>)</span> <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="c3">f</font> <a href="valued_1.html#NK26" title="VALUED_1:NK.26">(#)</a> <font color="Maroon" title="c2">c2</font></span>)</span> <a href="valued_1.html#K45" title="VALUED_1:func.45">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">g</font> <a href="valued_1.html#NK26" title="VALUED_1:NK.26">(#)</a> <font color="Maroon" title="c1">c1</font></span>)</span></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">c1</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">c2</font></span>)</span></span><br/>

<a NAME="E2:12"/><span class="lab"><font color="Green" title="E4">A2</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="valued_2.html#K14" title="VALUED_2:func.14">(/)</a> <font color="Maroon" title="c1">c1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c3">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 NAME="E3:12"/><span class="lab"><font color="Green" title="E5">A3</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">g</font> <a href="valued_2.html#K14" title="VALUED_2:func.14">(/)</a> <font color="Maroon" title="c2">c2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c4">g</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 NAME="E4:12"/><span class="lab"><font color="Green" title="E6">A4</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="valued_1.html#NK26" title="VALUED_1:NK.26">(#)</a> <font color="Maroon" title="c2">c2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c3">f</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="valued_1.html#D5" title="VALUED_1:def.5">VALUED_1:def 5</a></span>;<br/>
<a NAME="E5:12"/><span class="lab"><font color="Green" title="E7">A5</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">g</font> <a href="valued_1.html#NK26" title="VALUED_1:NK.26">(#)</a> <font color="Maroon" title="c1">c1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c4">g</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="valued_1.html#D5" title="VALUED_1:def.5">VALUED_1:def 5</a></span>;<br/>
<a NAME="E6:12"/><span class="lab"><font color="Green" title="E8">A6</font></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="c3">f</font> <a href="valued_2.html#K14" title="VALUED_2:func.14">(/)</a> <font color="Maroon" title="c1">c1</font></span>)</span> <a href="valued_1.html#K45" title="VALUED_1:func.45">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">g</font> <a href="valued_2.html#K14" title="VALUED_2:func.14">(/)</a> <font color="Maroon" title="c2">c2</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="valued_2.html#K14" title="VALUED_2:func.14">(/)</a> <font color="Maroon" title="c1">c1</font></span>)</span></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">g</font> <a href="valued_2.html#K14" title="VALUED_2:func.14">(/)</a> <font color="Maroon" title="c2">c2</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="valued_1.html#T12" title="VALUED_1:th.12">VALUED_1:12</a></span>;<br/>
<a NAME="E7:12"/><span class="lab"><font color="Green" title="E9">A7</font></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="c3">f</font> <a href="valued_1.html#NK26" title="VALUED_1:NK.26">(#)</a> <font color="Maroon" title="c2">c2</font></span>)</span> <a href="valued_1.html#K45" title="VALUED_1:func.45">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">g</font> <a href="valued_1.html#NK26" title="VALUED_1:NK.26">(#)</a> <font color="Maroon" title="c1">c1</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="valued_1.html#NK26" title="VALUED_1:NK.26">(#)</a> <font color="Maroon" title="c2">c2</font></span>)</span></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">g</font> <a href="valued_1.html#NK26" title="VALUED_1:NK.26">(#)</a> <font color="Maroon" title="c1">c1</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="valued_1.html#T12" title="VALUED_1:th.12">VALUED_1:12</a></span>;<br/>
<span class="kw">hence </span><a NAME="E8:12"/>
 <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="c3">f</font> <a href="valued_2.html#K14" title="VALUED_2:func.14">(/)</a> <font color="Maroon" title="c1">c1</font></span>)</span> <a href="valued_1.html#K45" title="VALUED_1:func.45">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">g</font> <a href="valued_2.html#K14" title="VALUED_2:func.14">(/)</a> <font color="Maroon" title="c2">c2</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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"><span class="p3">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="valued_1.html#NK26" title="VALUED_1:NK.26">(#)</a> <font color="Maroon" title="c2">c2</font></span>)</span> <a href="valued_1.html#K45" title="VALUED_1:func.45">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">g</font> <a href="valued_1.html#NK26" title="VALUED_1:NK.26">(#)</a> <font color="Maroon" title="c1">c1</font></span>)</span></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">c1</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">c2</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:12"><span class="lab"><font color="Green" title="E4">A2</font></span></a>, <a class="txt" href="#E3:12"><span class="lab"><font color="Green" title="E5">A3</font></span></a>, <a class="txt" href="#E4:12"><span class="lab"><font color="Green" title="E6">A4</font></span></a>, <a class="txt" href="#E5:12"><span class="lab"><font color="Green" title="E7">A5</font></span></a>, <a class="txt" href="#E6:12"><span class="lab"><font color="Green" title="E8">A6</font></span></a>, <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="c3">f</font> <a href="valued_2.html#K14" title="VALUED_2:func.14">(/)</a> <font color="Maroon" title="c1">c1</font></span>)</span> <a href="valued_1.html#K45" title="VALUED_1:func.45">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">g</font> <a href="valued_2.html#K14" title="VALUED_2:func.14">(/)</a> <font color="Maroon" title="c2">c2</font></span>)</span></span>)</span> or <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="valued_2.html#K14" title="VALUED_2:func.14">(/)</a> <font color="Maroon" title="c1">c1</font></span>)</span> <a href="valued_1.html#K45" title="VALUED_1:func.45">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">g</font> <a href="valued_2.html#K14" title="VALUED_2:func.14">(/)</a> <font color="Maroon" title="c2">c2</font></span>)</span></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"><span class="p3">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="valued_1.html#NK26" title="VALUED_1:NK.26">(#)</a> <font color="Maroon" title="c2">c2</font></span>)</span> <a href="valued_1.html#K45" title="VALUED_1:func.45">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">g</font> <a href="valued_1.html#NK26" title="VALUED_1:NK.26">(#)</a> <font color="Maroon" title="c1">c1</font></span>)</span></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">c1</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">c2</font></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="c5">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="c5">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="c3">f</font> <a href="valued_2.html#K14" title="VALUED_2:func.14">(/)</a> <font color="Maroon" title="c1">c1</font></span>)</span> <a href="valued_1.html#K45" title="VALUED_1:func.45">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">g</font> <a href="valued_2.html#K14" title="VALUED_2:func.14">(/)</a> <font color="Maroon" title="c2">c2</font></span>)</span></span>)</span> or <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="valued_2.html#K14" title="VALUED_2:func.14">(/)</a> <font color="Maroon" title="c1">c1</font></span>)</span> <a href="valued_1.html#K45" title="VALUED_1:func.45">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">g</font> <a href="valued_2.html#K14" title="VALUED_2:func.14">(/)</a> <font color="Maroon" title="c2">c2</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="valued_1.html#NK26" title="VALUED_1:NK.26">(#)</a> <font color="Maroon" title="c2">c2</font></span>)</span> <a href="valued_1.html#K45" title="VALUED_1:func.45">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">g</font> <a href="valued_1.html#NK26" title="VALUED_1:NK.26">(#)</a> <font color="Maroon" title="c1">c1</font></span>)</span></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">c1</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">c2</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font> )</span><br/>

<span class="kw">assume </span><a NAME="E9:12"/><span class="lab"><font color="Green" title="E10">A8</font></span>: 
<font color="Maroon" title="c5">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="c3">f</font> <a href="valued_2.html#K14" title="VALUED_2:func.14">(/)</a> <font color="Maroon" title="c1">c1</font></span>)</span> <a href="valued_1.html#K45" title="VALUED_1:func.45">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">g</font> <a href="valued_2.html#K14" title="VALUED_2:func.14">(/)</a> <font color="Maroon" title="c2">c2</font></span>)</span></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="c3">f</font> <a href="valued_2.html#K14" title="VALUED_2:func.14">(/)</a> <font color="Maroon" title="c1">c1</font></span>)</span> <a href="valued_1.html#K45" title="VALUED_1:func.45">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">g</font> <a href="valued_2.html#K14" title="VALUED_2:func.14">(/)</a> <font color="Maroon" title="c2">c2</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="valued_1.html#NK26" title="VALUED_1:NK.26">(#)</a> <font color="Maroon" title="c2">c2</font></span>)</span> <a href="valued_1.html#K45" title="VALUED_1:func.45">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">g</font> <a href="valued_1.html#NK26" title="VALUED_1:NK.26">(#)</a> <font color="Maroon" title="c1">c1</font></span>)</span></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">c1</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">c2</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font></span><br/>

<span class="kw">hence </span><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="valued_2.html#K14" title="VALUED_2:func.14">(/)</a> <font color="Maroon" title="c1">c1</font></span>)</span> <a href="valued_1.html#K45" title="VALUED_1:func.45">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">g</font> <a href="valued_2.html#K14" title="VALUED_2:func.14">(/)</a> <font color="Maroon" title="c2">c2</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="valued_2.html#K14" title="VALUED_2:func.14">(/)</a> <font color="Maroon" title="c1">c1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">g</font> <a href="valued_2.html#K14" title="VALUED_2:func.14">(/)</a> <font color="Maroon" title="c2">c2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="valued_1.html#T13" title="VALUED_1:th.13">VALUED_1:13</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font></span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <font color="Maroon" title="c1">c1</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">g</font> <a href="valued_2.html#K14" title="VALUED_2:func.14">(/)</a> <font color="Maroon" title="c2">c2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font></span>)</span>
<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="c3">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font></span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <font color="Maroon" title="c1">c1</font></span>)</span> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">g</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font></span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <font color="Maroon" title="c2">c2</font></span>)</span>
<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"><span class="p3">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">c2</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">g</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c1">c1</font></span>)</span></span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">c1</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">c2</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:12"><span class="lab"><font color="Green" title="E3">A1</font></span></a>, <a class="ref" href="xcmplx_1.html#T131" title="XCMPLX_1:th.131">XCMPLX_1:131</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">c2</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">g</font> <a href="valued_1.html#NK26" title="VALUED_1:NK.26">(#)</a> <font color="Maroon" title="c1">c1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font></span>)</span></span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">c1</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">c2</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="valued_1.html#T6" title="VALUED_1:th.6">VALUED_1:6</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="valued_1.html#NK26" title="VALUED_1:NK.26">(#)</a> <font color="Maroon" title="c2">c2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">g</font> <a href="valued_1.html#NK26" title="VALUED_1:NK.26">(#)</a> <font color="Maroon" title="c1">c1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font></span>)</span></span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">c1</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">c2</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="valued_1.html#T6" title="VALUED_1:th.6">VALUED_1:6</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="valued_1.html#NK26" title="VALUED_1:NK.26">(#)</a> <font color="Maroon" title="c2">c2</font></span>)</span> <a href="valued_1.html#K45" title="VALUED_1:func.45">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">g</font> <a href="valued_1.html#NK26" title="VALUED_1:NK.26">(#)</a> <font color="Maroon" title="c1">c1</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">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">c1</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">c2</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:12"><span class="lab"><font color="Green" title="E4">A2</font></span></a>, <a class="txt" href="#E3:12"><span class="lab"><font color="Green" title="E5">A3</font></span></a>, <a class="txt" href="#E4:12"><span class="lab"><font color="Green" title="E6">A4</font></span></a>, <a class="txt" href="#E5:12"><span class="lab"><font color="Green" title="E7">A5</font></span></a>, <a class="txt" href="#E6:12"><span class="lab"><font color="Green" title="E8">A6</font></span></a>, <a class="txt" href="#E7:12"><span class="lab"><font color="Green" title="E9">A7</font></span></a>, <a class="txt" href="#E9:12"><span class="lab"><font color="Green" title="E10">A8</font></span></a>, <a class="ref" href="valued_1.html#T13" title="VALUED_1:th.13">VALUED_1:13</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="valued_1.html#NK26" title="VALUED_1:NK.26">(#)</a> <font color="Maroon" title="c2">c2</font></span>)</span> <a href="valued_1.html#K45" title="VALUED_1:func.45">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">g</font> <a href="valued_1.html#NK26" title="VALUED_1:NK.26">(#)</a> <font color="Maroon" title="c1">c1</font></span>)</span></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">c1</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">c2</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">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>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
