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<span class="kw">set </span><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/>
<span class="kw">set </span><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/>
<span class="kw">set </span><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/>
<span class="kw">consider </span><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><span class="kw"> such that </span><br/><a NAME="E2:72_1_1"/>
<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>
 <span class="kw">and </span><br/><a NAME="E3:72_1_1"/><span class="lab"><font color="Green" title="E38">A1</font></span>: 
<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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="vectsp10.html#T29" target="_self" title="VECTSP10:th.29">Th29</a></span>;<br/>
<span class="kw">reconsider </span><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> <span class="kw">by</span> <span class="lab"><a class="ref" href="vectsp10.html#T24" target="_self" title="VECTSP10:th.24">Th24</a></span>;<br/>
<span class="kw">assume </span><a NAME="E5:72_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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E6:72_1_1"/><span class="kw">then </span>
 <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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="vectsp10.html#D7" target="_self" title="VECTSP10:def.7">Def7</a></span>;<br/>
<span class="kw">then </span> <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>
<span class="kw">by</span> <span class="lab"><a class="ref" href="hahnban1.html#T22" title="HAHNBAN1:th.22">HAHNBAN1:22</a></span>
<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>
<span class="kw">by</span> <span class="lab"><a class="ref" href="vectsp10.html#T36" target="_self" title="VECTSP10:th.36">Th36</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E8:72_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:72_1_1"><span class="lab"><font color="Green" title="E38">A1</font></span></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/>


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