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<span class="kw">let </span><font color="Maroon" title="c1">V</font> be   <a href="vectsp_1.html#NM7" title="VECTSP_1:NM.7">VectSp</a> of  <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</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">v</font>, <font color="Olive" title="b2">w</font> being  <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Vector</a> of <font color="Maroon" title="c1">V</font><br/> for <font color="Olive" title="b3">f</font> being  <a href="hermitan.html#V5" title="HERMITAN:attr.5">diagReR+0valued</a>  <a href="hermitan.html#NM3" title="HERMITAN:NM.3">hermitan-Form</a> of <font color="Maroon" title="c1">V</font> holds  <span class="p1"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b3">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Olive" title="b1">v</font>,<font color="Olive" title="b2">w</font></span>)</span></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="hermitan.html#K4" title="HERMITAN:func.4">signnorm</a> <font color="Olive" title="b3">f</font>,<font color="Olive" title="b1">v</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><a href="hermitan.html#K4" title="HERMITAN:func.4">signnorm</a> <font color="Olive" title="b3">f</font>,<font color="Olive" title="b2">w</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">v1</font>, <font color="Maroon" title="c3">w</font> be   <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Vector</a> of <font color="Maroon" title="c1">V</font>; <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="hermitan.html#V5" title="HERMITAN:attr.5">diagReR+0valued</a>  <a href="hermitan.html#NM3" title="HERMITAN:NM.3">hermitan-Form</a> of <font color="Maroon" title="c1">V</font> holds  <span class="p1"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c2">v1</font>,<font color="Maroon" title="c3">w</font></span>)</span></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="hermitan.html#K4" title="HERMITAN:func.4">signnorm</a> <font color="Olive" title="b1">f</font>,<font color="Maroon" title="c2">v1</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><a href="hermitan.html#K4" title="HERMITAN:func.4">signnorm</a> <font color="Olive" title="b1">f</font>,<font color="Maroon" title="c3">w</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c4">f</font> be   <a href="hermitan.html#V5" title="HERMITAN:attr.5">diagReR+0valued</a>  <a href="hermitan.html#NM3" title="HERMITAN:NM.3">hermitan-Form</a> of <font color="Maroon" title="c1">V</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c2">v1</font>,<font color="Maroon" title="c3">w</font></span>)</span></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="hermitan.html#K4" title="HERMITAN:func.4">signnorm</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c2">v1</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><a href="hermitan.html#K4" title="HERMITAN:func.4">signnorm</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c3">w</font></span>)</span></span><br/>





<span class="kw">set </span><font color="Maroon" title="c5">v4</font> = <font color="Maroon" title="c4">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c2">v1</font>,<font color="Maroon" title="c3">w</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c6">w1</font> = <font color="Maroon" title="c4">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c3">w</font>,<font color="Maroon" title="c2">v1</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c7">A</font> =  <a href="hermitan.html#K4" title="HERMITAN:func.4">signnorm</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c2">v1</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c8">B</font> = <span class="p1"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c3">w</font>,<font color="Maroon" title="c2">v1</font></span>)</span></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c9">C</font> =  <a href="hermitan.html#K4" title="HERMITAN:func.4">signnorm</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c3">w</font>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c10">A</font> =  <a href="hermitan.html#K4" title="HERMITAN:func.4">signnorm</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c2">v1</font>, <font color="Maroon" title="c11">B</font> = <span class="p1"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c3">w</font>,<font color="Maroon" title="c2">v1</font></span>)</span></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span>, <font color="Maroon" title="c12">C</font> =  <a href="hermitan.html#K4" title="HERMITAN:func.4">signnorm</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c3">w</font> as   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> ;<br/>
<a NAME="E2:95"/><span class="lab"><font color="Green" title="E42">A1</font></span>: 
( <font color="Maroon" title="c12">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a>  implies <font color="Maroon" title="c11">B</font> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c10">A</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c12">C</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="hermitan.html#T47" target="_self" title="HERMITAN:th.47">Th47</a></span>;<br/>
<a NAME="E3:95"/><span class="lab"><font color="Green" title="E43">A2</font></span>: 
 ex <font color="Olive" title="b1">a</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a>  st <br/>( <span class="p1"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><font color="Olive" title="b1">a</font></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp;  <a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">a</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c3">w</font>,<font color="Maroon" title="c2">v1</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c3">w</font>,<font color="Maroon" title="c2">v1</font></span>)</span></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span> &amp;  <a href="complex1.html#K4" title="COMPLEX1:func.4">Im</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">a</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c3">w</font>,<font color="Maroon" title="c2">v1</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="hermitan.html#T9" target="_self" title="HERMITAN:th.9">Th9</a></span>;<br/>
<a NAME="E4:95"/><span class="lab"><font color="Green" title="E44">A3</font></span>: 
( <font color="Maroon" title="c12">C</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  implies <font color="Maroon" title="c11">B</font> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c10">A</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c12">C</font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="95_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:95_1"/><span class="lab"><font color="Green" title="E45">A4</font></span>: 
<font color="Maroon" title="c12">C</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</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="c11">B</font> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c10">A</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c12">C</font></span><br/>

<span class="p1">(<span class="default"><font color="Maroon" title="c10">A</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c11">B</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c11">B</font> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <font color="Maroon" title="c12">C</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">C</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c11">B</font> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <font color="Maroon" title="c12">C</font></span>)</span> <a href="square_1.html#K4" title="SQUARE_1:func.4">^2</a> </span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c10">A</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c11">B</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p4">(<span class="default">2 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c11">B</font></span>)</span></span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <font color="Maroon" title="c12">C</font></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">C</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c11">B</font> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <font color="Maroon" title="c12">C</font></span>)</span> <a href="square_1.html#K4" title="SQUARE_1:func.4">^2</a> </span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="xcmplx_1.html#T75" title="XCMPLX_1:th.75">XCMPLX_1:75</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c10">A</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c11">B</font> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> 2</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <font color="Maroon" title="c12">C</font></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">C</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c11">B</font> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <font color="Maroon" title="c12">C</font></span>)</span> <a href="square_1.html#K4" title="SQUARE_1:func.4">^2</a> </span>)</span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c10">A</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2">(<span class="default">2 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c11">B</font> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <font color="Maroon" title="c12">C</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">C</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c11">B</font> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <font color="Maroon" title="c12">C</font></span>)</span> <a href="square_1.html#K4" title="SQUARE_1:func.4">^2</a> </span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="xcmplx_1.html#T75" title="XCMPLX_1:th.75">XCMPLX_1:75</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c10">A</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2">(<span class="default">2 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c11">B</font> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <font color="Maroon" title="c12">C</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">C</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c11">B</font> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p3">(<span class="default"><font color="Maroon" title="c12">C</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c12">C</font></span>)</span></span>)</span></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"><font color="Maroon" title="c10">A</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2">(<span class="default">2 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c11">B</font> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <font color="Maroon" title="c12">C</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c12">C</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c11">B</font> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span></span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p2">(<span class="default"><font color="Maroon" title="c12">C</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c12">C</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="xcmplx_1.html#T75" title="XCMPLX_1:th.75">XCMPLX_1:75</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c10">A</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2">(<span class="default">2 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c11">B</font> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <font color="Maroon" title="c12">C</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c11">B</font> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <font color="Maroon" title="c12">C</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:95_1"><span class="lab"><font color="Green" title="E45">A4</font></span></a>, <a class="ref" href="xcmplx_1.html#T92" title="XCMPLX_1:th.92">XCMPLX_1:92</a></span>
<br/>.= 
<font color="Maroon" title="c10">A</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c11">B</font> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <font color="Maroon" title="c12">C</font></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c10">A</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c12">C</font></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c11">B</font> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span></span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <font color="Maroon" title="c12">C</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:95_1"><span class="lab"><font color="Green" title="E45">A4</font></span></a>, <a class="ref" href="xcmplx_1.html#T128" title="XCMPLX_1:th.128">XCMPLX_1:128</a></span>
;<br/>
<a NAME="E3:95_1"/><span class="kw">then </span>
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">A</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c12">C</font></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">B</font> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:95"><span class="lab"><font color="Green" title="E43">A2</font></span></a>, <a class="txt" href="#E1:95_1"><span class="lab"><font color="Green" title="E45">A4</font></span></a>, <a class="ref" href="hermitan.html#T46" target="_self" title="HERMITAN:th.46">Th46</a></span>;<br/>
<a NAME="E4:95_1"/><span class="kw">then </span>
<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">B</font> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c10">A</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c12">C</font></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c11">B</font> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">B</font> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_1.html#T8" title="XREAL_1:th.8">XREAL_1:8</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:95_1"/>
<font color="Maroon" title="c11">B</font> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c10">A</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c12">C</font>
 ; <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><span class="kw">end;</span></div>
<font color="Maroon" title="c11">B</font> = 
<span class="p1"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c2">v1</font>,<font color="Maroon" title="c3">w</font></span>)</span> <a href="complfld.html#K2" title="COMPLFLD:func.2">*'</a> </span>)</span></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="hermitan.html#D5" target="_self" title="HERMITAN:def.5">Def5</a></span>
<br/>.= 
<span class="p1"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c2">v1</font>,<font color="Maroon" title="c3">w</font></span>)</span></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="complex1.html#T139" title="COMPLEX1:th.139">COMPLEX1:139</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E6:95"/>
<span class="p1"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c2">v1</font>,<font color="Maroon" title="c3">w</font></span>)</span></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="hermitan.html#K4" title="HERMITAN:func.4">signnorm</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c2">v1</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><a href="hermitan.html#K4" title="HERMITAN:func.4">signnorm</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c3">w</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:95"><span class="lab"><font color="Green" title="E42">A1</font></span></a>, <a class="txt" href="#E4:95"><span class="lab"><font color="Green" title="E44">A3</font></span></a>, <a class="ref" href="hermitan.html#D7" target="_self" title="HERMITAN:def.7">Def7</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/>


</div>
