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

<span class="kw">set </span><font color="Maroon" title="c3">vq</font> =  <a href="vectsp10.html#K6" title="VECTSP10:func.6">VectQuot</a> <font color="Maroon" title="c1">V</font>,<span class="p1">(<span class="default"><a href="bilinear.html#K15" title="BILINEAR:func.15">LKer</a> <font color="Maroon" title="c2">f</font></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c4">vr</font> =  <a href="vectsp10.html#K6" title="VECTSP10:func.6">VectQuot</a> <font color="Maroon" title="c1">V</font>,<span class="p1">(<span class="default"><a href="bilinear.html#K16" title="BILINEAR:func.16">RKer</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="hermitan.html#K3" title="HERMITAN:func.3">*'</a> </span>)</span></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c5">qh</font> =  <a href="hermitan.html#K9" title="HERMITAN:func.9">ScalarForm</a> <font color="Maroon" title="c2">f</font>;<br/>
<span class="lab"><font color="Green" title="E61">A1</font></span>:  <a href="bilinear.html#K12" title="BILINEAR:func.12">leftker</a> <span class="p1">(<span class="default"><a href="hermitan.html#K9" title="HERMITAN:func.9">ScalarForm</a> <font color="Maroon" title="c2">f</font></span>)</span> = 
 <a href="bilinear.html#K12" title="BILINEAR:func.12">leftker</a> <span class="p1">(<span class="default"><a href="hermitan.html#K8" title="HERMITAN:func.8">Q*Form</a> <font color="Maroon" title="c2">f</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="hermitan.html#T69" target="_self" title="HERMITAN:th.69">Th69</a></span>
<br/>.= 
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <span class="p3">(<span class="default"><a href="vectsp10.html#K6" title="VECTSP10:func.6">VectQuot</a> <font color="Maroon" title="c1">V</font>,<span class="p4">(<span class="default"><a href="bilinear.html#K15" title="BILINEAR:func.15">LKer</a> <font color="Maroon" title="c2">f</font></span>)</span></span>)</span></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="bilinear.html#D24" title="BILINEAR:def.24">BILINEAR:def 24</a></span>
;<br/>
 <a href="bilinear.html#K13" title="BILINEAR:func.13">rightker</a> <span class="p1">(<span class="default"><a href="hermitan.html#K9" title="HERMITAN:func.9">ScalarForm</a> <font color="Maroon" title="c2">f</font></span>)</span> = 
 <a href="bilinear.html#K13" title="BILINEAR:func.13">rightker</a> <span class="p1">(<span class="default"><a href="hermitan.html#K8" title="HERMITAN:func.8">Q*Form</a> <font color="Maroon" title="c2">f</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="hermitan.html#T59" target="_self" title="HERMITAN:th.59">Th59</a></span>
<br/>.= 
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <span class="p3">(<span class="default"><a href="vectsp10.html#K6" title="VECTSP10:func.6">VectQuot</a> <font color="Maroon" title="c1">V</font>,<span class="p4">(<span class="default"><a href="bilinear.html#K16" title="BILINEAR:func.16">RKer</a> <span class="p5">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="hermitan.html#K3" title="HERMITAN:func.3">*'</a> </span>)</span></span>)</span></span>)</span></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="bilinear.html#D25" title="BILINEAR:def.25">BILINEAR:def 25</a></span>
<br/>.= 
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <span class="p3">(<span class="default"><a href="vectsp10.html#K6" title="VECTSP10:func.6">VectQuot</a> <font color="Maroon" title="c1">V</font>,<span class="p4">(<span class="default"><a href="bilinear.html#K15" title="BILINEAR:func.15">LKer</a> <font color="Maroon" title="c2">f</font></span>)</span></span>)</span></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="hermitan.html#T59" target="_self" title="HERMITAN:th.59">Th59</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E3:131_1_1"/><span class="lab"><font color="Green" title="E62">A2</font></span>: 
( not  <a href="hermitan.html#K9" title="HERMITAN:func.9">ScalarForm</a> <font color="Maroon" title="c2">f</font> is  <a href="bilinear.html#V5" title="BILINEAR:attr.5">degenerated-on-left</a>  &amp; not  <a href="hermitan.html#K9" title="HERMITAN:func.9">ScalarForm</a> <font color="Maroon" title="c2">f</font> is  <a href="bilinear.html#V6" title="BILINEAR:attr.6">degenerated-on-right</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:131_1_1"><span class="lab"><font color="Green" title="E61">A1</font></span></a>, <a class="ref" href="bilinear.html#D24" title="BILINEAR:def.24">BILINEAR:def 24</a>, <a class="ref" href="bilinear.html#D25" title="BILINEAR:def.25">BILINEAR:def 25</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="hermitan.html#K9" title="HERMITAN:func.9">ScalarForm</a> <font color="Maroon" title="c2">f</font> is  <a href="hermitan.html#V6" title="HERMITAN:attr.6">positivediagvalued</a> </span><br/>

<span class="kw">let </span><font color="Maroon" title="c6">A</font> be   <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Vector</a> of <span class="p1">(<span class="default"><a href="vectsp10.html#K6" title="VECTSP10:func.6">VectQuot</a> <font color="Maroon" title="c1">V</font>,<span class="p2">(<span class="default"><a href="bilinear.html#K15" title="BILINEAR:func.15">LKer</a> <font color="Maroon" title="c2">f</font></span>)</span></span>)</span>; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="hermitan.html#D13" target="_self" title="HERMITAN:def.13">HERMITAN:def 13</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="c6">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <span class="p1">(<span class="default"><a href="vectsp10.html#K6" title="VECTSP10:func.6">VectQuot</a> <font color="Maroon" title="c1">V</font>,<span class="p2">(<span class="default"><a href="bilinear.html#K15" title="BILINEAR:func.15">LKer</a> <font color="Maroon" title="c2">f</font></span>)</span></span>)</span> implies  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="hermitan.html#K9" title="HERMITAN:func.9">ScalarForm</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c6">A</font>,<font color="Maroon" title="c6">A</font></span>)</span> )</span><br/>

<span class="kw">assume </span><a NAME="E4:131_1_1"/>
<font color="Maroon" title="c6">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <span class="p1">(<span class="default"><a href="vectsp10.html#K6" title="VECTSP10:func.6">VectQuot</a> <font color="Maroon" title="c1">V</font>,<span class="p2">(<span class="default"><a href="bilinear.html#K15" title="BILINEAR:func.15">LKer</a> <font color="Maroon" title="c2">f</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">  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="hermitan.html#K9" title="HERMITAN:func.9">ScalarForm</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c6">A</font>,<font color="Maroon" title="c6">A</font></span>)</span></span><br/>

<a NAME="E5:131_1_1"/><span class="kw">then </span>
 <a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="hermitan.html#K9" title="HERMITAN:func.9">ScalarForm</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c6">A</font>,<font color="Maroon" title="c6">A</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:131_1_1"><span class="lab"><font color="Green" title="E62">A2</font></span></a>, <a class="ref" href="hermitan.html#T61" target="_self" title="HERMITAN:th.61">Th61</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:131_1_1"/>
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="hermitan.html#K9" title="HERMITAN:func.9">ScalarForm</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c6">A</font>,<font color="Maroon" title="c6">A</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><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>
