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

<b>set </b><font color="Maroon" title="c4">W</font> =  <a href="vectsp10.html#K9" title="VECTSP10:func.9">Ker</a> <font color="Maroon" title="c3">f</font>;<br/>
<b>set </b><font color="Maroon" title="c5">qf</font> =  <a href="vectsp10.html#K11" title="VECTSP10:func.11">CQFunctional</a> <font color="Maroon" title="c3">f</font>;<br/>
<b>set </b><font color="Maroon" title="c6">qv</font> =  <a href="vectsp10.html#K6" title="VECTSP10:func.6">VectQuot</a> <font color="Maroon" title="c2">V</font>,<span class="p1">(<span class="default"><a href="vectsp10.html#K9" title="VECTSP10:func.9">Ker</a> <font color="Maroon" title="c3">f</font></span>)</span>;<br/>
<b>assume </b><a NAME="E1:72_1_1"/>
 <a href="vectsp10.html#K11" title="VECTSP10:func.11">CQFunctional</a> <font color="Maroon" title="c3">f</font> is <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:72_1_1"/><b>then </b><i><font color="Green" title="E38">A1</font></i>: 
 <a href="vectsp10.html#K11" title="VECTSP10:func.11">CQFunctional</a> <font color="Maroon" title="c3">f</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="hahnban1.html#K7" title="HAHNBAN1:func.7">0Functional</a> <span class="p1">(<span class="default"><a href="vectsp10.html#K6" title="VECTSP10:func.6">VectQuot</a> <font color="Maroon" title="c2">V</font>,<span class="p2">(<span class="default"><a href="vectsp10.html#K9" title="VECTSP10:func.9">Ker</a> <font color="Maroon" title="c3">f</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="vectsp10.html#D7" target="_self" title="VECTSP10:def.7">Def7</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c7">v</font> being   <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Vector</a> of <font color="Maroon" title="c2">V</font><b> such that </b><br/><a NAME="E4:72_1_1"/><i><font color="Green" title="E39">A2</font></i>: 
( <font color="Maroon" title="c7">v</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> <font color="Maroon" title="c2">V</font> &amp; <font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">v</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> <font color="Maroon" title="c1">K</font> )
 <b>by </b><i><a class="ref" href="vectsp10.html#T29" target="_self" title="VECTSP10:th.29">Th29</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c8">cv</font> = <font color="Maroon" title="c7">v</font> <a href="vectsp_4.html#K3" title="VECTSP_4:func.3">+</a> <span class="p1">(<span class="default"><a href="vectsp10.html#K9" title="VECTSP10:func.9">Ker</a> <font color="Maroon" title="c3">f</font></span>)</span> as   <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="c2">V</font>,<span class="p2">(<span class="default"><a href="vectsp10.html#K9" title="VECTSP10:func.9">Ker</a> <font color="Maroon" title="c3">f</font></span>)</span></span>)</span> <b>by </b><i><a class="ref" href="vectsp10.html#T24" target="_self" title="VECTSP10:th.24">Th24</a></i>;<br/>
 <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">K</font> = 
<span class="p1">(<span class="default"><a href="vectsp10.html#K11" title="VECTSP10:func.11">CQFunctional</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">cv</font>
<b>by </b><i><a class="txt" href="vectsp10.html#E2:72_1_1"><i><font color="Green" title="E38">A1</font></i></a>, <a class="ref" href="hahnban1.html#T22" title="HAHNBAN1:th.22">HAHNBAN1:22</a></i>
<br/>.= 
<font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">v</font>
<b>by </b><i><a class="ref" href="vectsp10.html#T36" target="_self" title="VECTSP10:th.36">Th36</a></i>
;<br/>
<b>hence </b><a NAME="E7:72_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="vectsp10.html#E4:72_1_1"><i><font color="Green" title="E39">A2</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
