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<div class="add">

<b>let </b><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> ;<br/><b>let </b><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>;<br/><b>let </b><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>;<br/><b>let </b><font color="Maroon" title="c5">r</font> be   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>;<br/><b>let </b><font color="Maroon" title="c6">a</font> be   <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> ;<br/>









<b>assume </b><a NAME="E1:91"/><i><font color="Green" title="E41">A1</font></i>: 
( <span class="p1"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><font color="Maroon" title="c6">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="Maroon" title="c6">a</font> <a href="group_1.html#K10" title="GROUP_1:func.10">*</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="Maroon" title="c6">a</font> <a href="group_1.html#K10" title="GROUP_1:func.10">*</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> 0 )
 ;<br/>

<b>set </b><font color="Maroon" title="c7">v3</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="c2">v1</font>;<br/>
<b>set </b><font color="Maroon" title="c8">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/>
<b>set </b><font color="Maroon" title="c9">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/>
<b>set </b><font color="Maroon" title="c10">w2</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="c3">w</font>;<br/>
<b>set </b><font color="Maroon" title="c11">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/>
<b>set </b><font color="Maroon" title="c12">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/>
<b>set </b><font color="Maroon" title="c13">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/>
<i><font color="Green" title="E42">A2</font></i>: <span class="p1">(<span class="default"><font color="Maroon" title="c6">a</font> <a href="complfld.html#K2" title="COMPLFLD:func.2">*'</a> </span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p1">(<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 class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c6">a</font> <a href="complfld.html#K2" title="COMPLFLD:func.2">*'</a> </span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <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></span>)</span> <a href="complfld.html#K2" title="COMPLFLD:func.2">*'</a> </span>)</span> <a href="complfld.html#K2" title="COMPLFLD:func.2">*'</a> 

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c6">a</font> <a href="complfld.html#K2" title="COMPLFLD:func.2">*'</a> </span>)</span> <a href="complfld.html#K2" title="COMPLFLD:func.2">*'</a> </span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <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>)</span> <a href="complfld.html#K2" title="COMPLFLD:func.2">*'</a> 
<b>by </b><i><a class="ref" href="complfld.html#T90" title="COMPLFLD:th.90">COMPLFLD:90</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">a</font> <a href="group_1.html#K10" title="GROUP_1:func.10">*</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="complfld.html#K2" title="COMPLFLD:func.2">*'</a> 
<b>by </b><i><a class="ref" href="hermitan.html#D5" target="_self" title="HERMITAN:def.5">Def5</a></i>
;<br/>
<a NAME="E3:91"/><i><font color="Green" title="E43">A3</font></i>: 
<font color="Maroon" title="c4">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">v1</font> <a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><font color="Maroon" title="c5">r</font>,0</span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c6">a</font></span>)</span> <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <font color="Maroon" title="c3">w</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">v1</font> <a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><font color="Maroon" title="c5">r</font>,0</span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c6">a</font></span>)</span> <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <font color="Maroon" title="c3">w</font></span>)</span></span>)</span> <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="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="c2">v1</font></span>)</span> <a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <span class="p3">(<span class="default"><span class="p4"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><font color="Maroon" title="c5">r</font>,0</span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">a</font> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p5">(<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></span>)</span></span>)</span> <a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <span class="p2">(<span class="default"><span class="p3"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><font color="Maroon" title="c5">r</font>,0</span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c6">a</font> <a href="complfld.html#K2" title="COMPLFLD:func.2">*'</a> </span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p4">(<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>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">r</font> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span>,0</span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</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="c3">w</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="hermitan.html#E1:91"><i><font color="Green" title="E41">A1</font></i></a>, <a class="ref" href="hermitan.html#T45" target="_self" title="HERMITAN:th.45">Th45</a></i>;<br/>
<a NAME="E4:91"/><i><font color="Green" title="E44">A4</font></i>: 
(  <a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <span class="p1"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><font color="Maroon" title="c5">r</font>,0</span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">r</font> &amp;  <a href="complex1.html#K4" title="COMPLEX1:func.4">Im</a> <span class="p1"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><font color="Maroon" title="c5">r</font>,0</span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0 )
 
<b>by </b><i><a class="ref" href="complex1.html#T28" title="COMPLEX1:th.28">COMPLEX1:28</a></i>;<br/>
<a NAME="E5:91"/><b>then </b><i><font color="Green" title="E45">A5</font></i>: 
 <a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <span class="p1">(<span class="default"><span class="p2"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><font color="Maroon" title="c5">r</font>,0</span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">a</font> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <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="c3">w</font>,<font color="Maroon" title="c2">v1</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">r</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</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>
 
<b>by </b><i><a class="txt" href="hermitan.html#E1:91"><i><font color="Green" title="E41">A1</font></i></a>, <a class="ref" href="hermitan.html#T11" target="_self" title="HERMITAN:th.11">Th11</a></i>;<br/>
<i><font color="Green" title="E46">A6</font></i>:  <a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <span class="p1">(<span class="default"><span class="p2"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><font color="Maroon" title="c5">r</font>,0</span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c6">a</font> <a href="complfld.html#K2" title="COMPLFLD:func.2">*'</a> </span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <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></span>)</span></span>)</span> = 
<font color="Maroon" title="c5">r</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p1">(<span class="default"><a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c6">a</font> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p4">(<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="complfld.html#K2" title="COMPLFLD:func.2">*'</a> </span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="hermitan.html#E2:91"><i><font color="Green" title="E42">A2</font></i></a>, <a class="txt" href="hermitan.html#E4:91"><i><font color="Green" title="E44">A4</font></i></a>, <a class="ref" href="hermitan.html#T11" target="_self" title="HERMITAN:th.11">Th11</a></i>
<br/>.= 
<font color="Maroon" title="c5">r</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</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>
<b>by </b><i><a class="txt" href="hermitan.html#E1:91"><i><font color="Green" title="E41">A1</font></i></a>, <a class="ref" href="complex1.html#T112" title="COMPLEX1:th.112">COMPLEX1:112</a></i>
;<br/>
<a NAME="E7:91"/>
(  <a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <span class="p1"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">r</font> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span>,0</span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">r</font> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a>  &amp;  <a href="complex1.html#K4" title="COMPLEX1:func.4">Im</a> <span class="p1"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">r</font> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span>,0</span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0 )
 
<b>by </b><i><a class="ref" href="complex1.html#T28" title="COMPLEX1:th.28">COMPLEX1:28</a></i>;<br/>
<a NAME="E8:91"/><b>then </b>
 <a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <span class="p1">(<span class="default"><span class="p2"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">r</font> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span>,0</span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</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="c3">w</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">r</font> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </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>
 
<b>by </b><i><a class="ref" href="hermitan.html#T11" target="_self" title="HERMITAN:th.11">Th11</a></i>;<br/>
<b>then </b> <a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">v1</font> <a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><font color="Maroon" title="c5">r</font>,0</span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c6">a</font></span>)</span> <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <font color="Maroon" title="c3">w</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">v1</font> <a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><font color="Maroon" title="c5">r</font>,0</span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c6">a</font></span>)</span> <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <font color="Maroon" title="c3">w</font></span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<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="c2">v1</font></span>)</span> <a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <span class="p4">(<span class="default"><span class="p5"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><font color="Maroon" title="c5">r</font>,0</span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c6">a</font> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p0">(<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></span>)</span></span>)</span> <a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <span class="p3">(<span class="default"><span class="p4"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><font color="Maroon" title="c5">r</font>,0</span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c6">a</font> <a href="complfld.html#K2" title="COMPLFLD:func.2">*'</a> </span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p5">(<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>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<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> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">r</font> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="hermitan.html#E3:91"><i><font color="Green" title="E43">A3</font></i></a>, <a class="ref" href="hahnban1.html#T16" title="HAHNBAN1:th.16">HAHNBAN1:16</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <span class="p3">(<span class="default"><span class="p4">(<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="c2">v1</font></span>)</span> <a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <span class="p4">(<span class="default"><span class="p5"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><font color="Maroon" title="c5">r</font>,0</span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c6">a</font> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p0">(<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></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">r</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p3"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><span class="p4">(<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></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<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> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">r</font> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="hermitan.html#E6:91"><i><font color="Green" title="E46">A6</font></i></a>, <a class="ref" href="hermitan.html#T10" target="_self" title="HERMITAN:th.10">Th10</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<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#K6" title="XCMPLX_0:func.6">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">r</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p4"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><span class="p5">(<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></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">r</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p3"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><span class="p4">(<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></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<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> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">r</font> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="hermitan.html#E5:91"><i><font color="Green" title="E45">A5</font></i></a>, <a class="ref" href="hermitan.html#T10" target="_self" title="HERMITAN:th.10">Th10</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<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#K6" title="XCMPLX_0:func.6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p4"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><span class="p5">(<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></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <font color="Maroon" title="c5">r</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<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> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">r</font> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span></span>)</span>

;<br/>
<b>hence </b><a NAME="E10:91"/>
(  <a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">v1</font> <a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><font color="Maroon" title="c5">r</font>,0</span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c6">a</font></span>)</span> <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <font color="Maroon" title="c3">w</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">v1</font> <a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><font color="Maroon" title="c5">r</font>,0</span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c6">a</font></span>)</span> <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <font color="Maroon" title="c3">w</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<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#K6" title="XCMPLX_0:func.6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p4"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><span class="p5">(<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></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <font color="Maroon" title="c5">r</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<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> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">r</font> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span></span>)</span> &amp; 0 <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"><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#K6" title="XCMPLX_0:func.6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p4"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><span class="p5">(<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></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <font color="Maroon" title="c5">r</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<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> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">r</font> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span></span>)</span> )
 <b>by </b><i><a class="ref" href="hermitan.html#D7" target="_self" title="HERMITAN:def.7">Def7</a></i>;<br/>


</div>
