<?xml version="1.0"?>
<div class="add">

<b>set </b><font color="Maroon">c<sub>3</sub></font> =  <a href="hermitan.html#K5" target="_self">quasinorm</a> <font color="Maroon">c<sub>2</sub></font>;<br/>
<a NAME="E1:102_1_1"/><i><font color="Green">E52</font></i>: 
 <a href="hermitan.html#K5" target="_self">quasinorm</a> <font color="Maroon">c<sub>2</sub></font> is <a href="hahnban1.html#V4">subadditive</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="102_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font> be   <a href="vectsp_1.html#NM5">Vector</a> of <font color="Maroon">c<sub>1</sub></font>; <i><font color="Red">:: according to </font></i><a class="ref" href="hahnban1.html#D16">HAHNBAN1:def 16</a><br/>

<b>set </b><font color="Maroon">c<sub>6</sub></font> =  <a href="hermitan.html#K4" target="_self">signnorm</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>7</sub></font> =  <a href="hermitan.html#K4" target="_self">signnorm</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>8</sub></font> =  <a href="hermitan.html#K4" target="_self">signnorm</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>;<br/>
<a NAME="E1:102_1_1_1"/><i><font color="Green">E53</font></i>: 
(  <a href="hermitan.html#K4" target="_self">signnorm</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="complex1.html#K3">Re</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="binop_1.html#K2">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> &amp; 0 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="complex1.html#K3">Re</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="binop_1.html#K2">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><a href="hermitan.html#K5" target="_self">quasinorm</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="square_1.html#K6">sqrt</a> <span class="p1">(<span class="default"><a href="hermitan.html#K4" target="_self">signnorm</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> &amp;  <a href="hermitan.html#K4" target="_self">signnorm</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="complex1.html#K3">Re</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> &amp; 0 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="complex1.html#K3">Re</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="hermitan.html#K5" target="_self">quasinorm</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="square_1.html#K6">sqrt</a> <span class="p1">(<span class="default"><a href="hermitan.html#K4" target="_self">signnorm</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> &amp;  <a href="hermitan.html#K4" target="_self">signnorm</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="complex1.html#K3">Re</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> &amp; 0 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="complex1.html#K3">Re</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="hermitan.html#K5" target="_self">quasinorm</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="square_1.html#K6">sqrt</a> <span class="p1">(<span class="default"><a href="hermitan.html#K4" target="_self">signnorm</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> )
 
<b>by </b><i><a class="ref" href="hermitan.html#D7" target="_self">Def7</a>, <a class="ref" href="hermitan.html#D10" target="_self">Def10</a></i>;<br/>
<a NAME="E2:102_1_1_1"/><b>then </b>
( 0 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="hermitan.html#K5" target="_self">quasinorm</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>4</sub></font> &amp; 0 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="hermitan.html#K5" target="_self">quasinorm</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>5</sub></font> )
 
<b>by </b><i><a class="ref" href="square_1.html#D4">SQUARE_1:def 4</a></i>;<br/>
<a NAME="E3:102_1_1_1"/><b>then </b><i><font color="Green">E54</font></i>: 
0 <a href="real_1.html#K3">+</a> 0 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="hermitan.html#K5" target="_self">quasinorm</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="hermitan.html#K5" target="_self">quasinorm</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="xreal_1.html#T9">XREAL_1:9</a></i>;<br/>
<a NAME="E4:102_1_1_1"/>
 <a href="hermitan.html#K4" target="_self">signnorm</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p3">(<span class="default"><a href="hermitan.html#K4" target="_self">signnorm</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p3">(<span class="default"><a href="hermitan.html#K4" target="_self">signnorm</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="square_1.html#K3">^2</a> 
 
<b>by </b><i><a class="ref" href="hermitan.html#T50" target="_self">Th50</a></i>;<br/>
<a NAME="E5:102_1_1_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="hermitan.html#K5" target="_self">quasinorm</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="square_1.html#K7">sqrt</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="hermitan.html#K5" target="_self">quasinorm</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="hermitan.html#K5" target="_self">quasinorm</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span>
 
<b>by </b><i><a class="txt" href="hermitan.html#E1:102_1_1_1"><i><font color="Green">E53</font></i></a>, <a class="ref" href="square_1.html#T94">SQUARE_1:94</a></i>;<br/>
<b>hence </b><a NAME="E6:102_1_1_1"/>
<span class="p1">(<span class="default"><a href="hermitan.html#K5" target="_self">quasinorm</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="hermitan.html#K5" target="_self">quasinorm</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="hermitan.html#K5" target="_self">quasinorm</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="hermitan.html#E3:102_1_1_1"><i><font color="Green">E54</font></i></a>, <a class="ref" href="square_1.html#T89">SQUARE_1:89</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E2:102_1_1"/>
 <a href="hermitan.html#K5" target="_self">quasinorm</a> <font color="Maroon">c<sub>2</sub></font> is <a href="hahnban1.html#V7">homogeneous</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="102_1_1_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="vectsp_1.html#NM5">Vector</a> of <font color="Maroon">c<sub>1</sub></font>; <i><font color="Red">:: according to </font></i><a class="ref" href="hahnban1.html#D19">HAHNBAN1:def 19</a><br/><b>let </b><font color="Maroon">c<sub>5</sub></font> be   <a href="vectsp_1.html#NM4">Scalar</a> of ;<br/>



<i><font color="Green">E53</font></i>: <font color="Maroon">c<sub>2</sub></font> <a href="binop_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="vectsp_1.html#K6">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="vectsp_1.html#K6">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> = 
<font color="Maroon">c<sub>5</sub></font> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="vectsp_1.html#K6">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="bilinear.html#T32">BILINEAR:32</a></i>
<br/>.= 
<font color="Maroon">c<sub>5</sub></font> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="complfld.html#K2">*'</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="hermitan.html#T30" target="_self">Th30</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="complfld.html#K2">*'</a> </span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="group_1.html#D4">GROUP_1:def 4</a></i>
<br/>.= 
<span class="p1"><a href="hahnban1.html#K1">[**</a><span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="complfld.html#K3">|.</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="complfld.html#K3">.|</a></span> <a href="square_1.html#K5">^2</a> </span>)</span>,0</span><a href="hahnban1.html#K1">**]</a></span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="hermitan.html#T16" target="_self">Th16</a></i>
<br/>.= 
<span class="p1"><a href="hahnban1.html#K1">[**</a><span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="complfld.html#K3">|.</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="complfld.html#K3">.|</a></span> <a href="square_1.html#K5">^2</a> </span>)</span>,0</span><a href="hahnban1.html#K1">**]</a></span> <a href="group_1.html#K10">*</a> <span class="p1"><a href="hahnban1.html#K1">[**</a><span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K3">Re</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="complex1.html#K4">Im</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span><a href="hahnban1.html#K1">**]</a></span>
<b>by </b><i><a class="ref" href="comptrig.html#T9">COMPTRIG:9</a></i>
<br/>.= 
<span class="p1"><a href="hahnban1.html#K1">[**</a><span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="complfld.html#K3">|.</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="complfld.html#K3">.|</a></span> <a href="square_1.html#K5">^2</a> </span>)</span>,0</span><a href="hahnban1.html#K1">**]</a></span> <a href="group_1.html#K10">*</a> <span class="p1"><a href="hahnban1.html#K1">[**</a><span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K3">Re</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span>,0</span><a href="hahnban1.html#K1">**]</a></span>
<b>by </b><i><a class="ref" href="hermitan.html#D6" target="_self">Def6</a></i>
<br/>.= 
<span class="p1"><a href="hahnban1.html#K1">[**</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4"><a href="complfld.html#K3">|.</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="complfld.html#K3">.|</a></span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><a href="complex1.html#K3">Re</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span>,0</span><a href="hahnban1.html#K1">**]</a></span>
<b>by </b><i><a class="ref" href="hermitan.html#T15" target="_self">Th15</a></i>
;<br/>
<a NAME="E2:102_1_1_2"/><i><font color="Green">E54</font></i>: 
( 0 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1"><a href="complfld.html#K3">|.</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="complfld.html#K3">.|</a></span> <a href="square_1.html#K5">^2</a>  &amp; 0 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1"><a href="complfld.html#K3">|.</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="complfld.html#K3">.|</a></span> &amp; 0 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="complex1.html#K3">Re</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> )
 
<b>by </b><i><a class="ref" href="hermitan.html#D7" target="_self">Def7</a>, <a class="ref" href="complex1.html#T132">COMPLEX1:132</a>, <a class="ref" href="xreal_1.html#T65">XREAL_1:65</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><a href="hermitan.html#K5" target="_self">quasinorm</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="vectsp_1.html#K6">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> = 
 <a href="square_1.html#K6">sqrt</a> <span class="p1">(<span class="default"><a href="hermitan.html#K4" target="_self">signnorm</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="vectsp_1.html#K6">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="hermitan.html#D10" target="_self">Def10</a></i>
<br/>.= 
 <a href="square_1.html#K7">sqrt</a> <span class="p1">(<span class="default"><a href="complex1.html#K3">Re</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="binop_1.html#K2">.</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="vectsp_1.html#K6">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="vectsp_1.html#K6">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span>

<br/>.= 
 <a href="square_1.html#K7">sqrt</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="complfld.html#K3">|.</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="complfld.html#K3">.|</a></span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><a href="complex1.html#K3">Re</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="hermitan.html#E1:102_1_1_2"><i><font color="Green">E53</font></i></a>, <a class="ref" href="complex1.html#T28">COMPLEX1:28</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2">(<span class="default"><span class="p3"><a href="complfld.html#K3">|.</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="complfld.html#K3">.|</a></span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2">(<span class="default"><a href="complex1.html#K3">Re</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="hermitan.html#E2:102_1_1_2"><i><font color="Green">E54</font></i></a>, <a class="ref" href="square_1.html#T97">SQUARE_1:97</a></i>
<br/>.= 
<span class="p1"><a href="complfld.html#K3">|.</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="complfld.html#K3">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2">(<span class="default"><a href="complex1.html#K3">Re</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="hermitan.html#E2:102_1_1_2"><i><font color="Green">E54</font></i></a>, <a class="ref" href="square_1.html#T89">SQUARE_1:89</a></i>
<br/>.= 
<span class="p1"><a href="complfld.html#K3">|.</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="complfld.html#K3">.|</a></span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p2">(<span class="default"><a href="hermitan.html#K4" target="_self">signnorm</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span>

<br/>.= 
<span class="p1"><a href="complfld.html#K3">|.</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="complfld.html#K3">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="hermitan.html#K5" target="_self">quasinorm</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="hermitan.html#D10" target="_self">Def10</a></i>
;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:102_1_1"/>
 <a href="hermitan.html#K5" target="_self">quasinorm</a> <font color="Maroon">c<sub>2</sub></font> is   <a href="hahnban1.html#NM4">Semi-Norm</a> of <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="hermitan.html#E1:102_1_1"><i><font color="Green">E52</font></i></a></i>;<br/>


</div>
