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

<b>set </b><font color="Maroon">W</font> =  <a href="vectsp10.html#K9">Ker</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="hermitan.html#K1" target="_self">*'</a> </span>)</span>;<br/>
<b>set </b><font color="Maroon">qf</font> =  <a href="hermitan.html#K2" target="_self">QcFunctional</a> <font color="Maroon">f</font>;<br/>
<b>set </b><font color="Maroon">qv</font> =  <a href="vectsp10.html#K6">VectQuot</a> <font color="Maroon">V</font>,<span class="p1">(<span class="default"><a href="vectsp10.html#K9">Ker</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="hermitan.html#K1" target="_self">*'</a> </span>)</span></span>)</span>;<br/>
<b>assume </b><a NAME="E1:42_1_1"/>
 <a href="hermitan.html#K2" target="_self">QcFunctional</a> <font color="Maroon">f</font> is <a href="funct_1.html#V3">constant</a>
 ;<br/>

<a NAME="E2:42_1_1"/><b>then </b><i><font color="Green">E30</font></i>: 
 <a href="hermitan.html#K2" target="_self">QcFunctional</a> <font color="Maroon">f</font> <a href="funct_2.html#R2">=</a>  <a href="hahnban1.html#K7">0Functional</a> <span class="p1">(<span class="default"><a href="vectsp10.html#K6">VectQuot</a> <font color="Maroon">V</font>,<span class="p2">(<span class="default"><a href="vectsp10.html#K9">Ker</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="hermitan.html#K1" target="_self">*'</a> </span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="vectsp10.html#D7">VECTSP10:def 7</a></i>;<br/>
<b>consider </b><font color="Maroon">v</font> being   <a href="vectsp_1.html#NM5">Vector</a> of <font color="Maroon">V</font><b> such that </b><br/><a NAME="E4:42_1_1"/><i><font color="Green">E31</font></i>: 
( <font color="Maroon">v</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">V</font> &amp; <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">v</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <a href="complfld.html#K1">F_Complex</a>  )
 <b>by </b><i><a class="ref" href="vectsp10.html#T29">VECTSP10:29</a></i>;<br/>
<b>reconsider </b><font color="Maroon">cv</font> = <font color="Maroon">v</font> <a href="vectsp_4.html#K3">+</a> <span class="p1">(<span class="default"><a href="vectsp10.html#K9">Ker</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="hermitan.html#K1" target="_self">*'</a> </span>)</span></span>)</span> as   <a href="vectsp_1.html#NM5">Vector</a> of <span class="p1">(<span class="default"><a href="vectsp10.html#K6">VectQuot</a> <font color="Maroon">V</font>,<span class="p2">(<span class="default"><a href="vectsp10.html#K9">Ker</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="hermitan.html#K1" target="_self">*'</a> </span>)</span></span>)</span></span>)</span> <b>by </b><i><a class="ref" href="vectsp10.html#T24">VECTSP10:24</a></i>;<br/>
 <a href="rlvect_1.html#K1">0.</a> <a href="complfld.html#K1">F_Complex</a>  = 
<span class="p1">(<span class="default"><a href="hermitan.html#K2" target="_self">QcFunctional</a> <font color="Maroon">f</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">cv</font>
<b>by </b><i>, <a class="ref" href="hahnban1.html#T22">HAHNBAN1:22</a></i>
<br/>.= 
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">v</font>
<b>by </b><i/>
;<br/>
<b>hence </b><a NAME="E7:42_1_1"/>
contradiction
 <b>by </b><i><a class="ref" href="hermitan.html#T2" target="_self">Th2</a></i>;<br/>


</div>
