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<b>assume </b><a NAME="E1:61_1_1"/><i><font color="Green" title="E32">A1</font></i>: 
<font color="Maroon" title="c2">V</font> <a href="hahnban1.html#K8" title="HAHNBAN1:func.8">*'</a>  is <a href="realset2.html#V3" title="REALSET2:attr.3">trivial</a>
 ;<br/>

<b>consider </b><font color="Maroon" title="c3">g</font> being  <a href="funct_1.html#V3" title="FUNCT_1:attr.3">V7</a> <a href="hahnban1.html#NM2" title="HAHNBAN1:NM.2">linear-Functional</a> of <font color="Maroon" title="c2">V</font>;<br/>
<a NAME="E3:61_1_1"/><i><font color="Green" title="E33">A2</font></i>: 
<font color="Maroon" title="c3">g</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="hahnban1.html#K7" title="HAHNBAN1:func.7">0Functional</a> <font color="Maroon" title="c2">V</font>
 
;<br/>
<b>reconsider </b><font color="Maroon" title="c4">g</font> = <font color="Maroon" title="c3">g</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">V</font> <a href="hahnban1.html#K8" title="HAHNBAN1:func.8">*'</a> </span>)</span> <b>by </b><i><a class="ref" href="hahnban1.html#D14" title="HAHNBAN1:def.14">HAHNBAN1:def 14</a></i>;<br/>
<a NAME="E5:61_1_1"/>
<font color="Maroon" title="c4">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">V</font> <a href="hahnban1.html#K8" title="HAHNBAN1:func.8">*'</a> </span>)</span>
 
<b>by </b><i><a class="txt" href="vectsp10.html#E1:61_1_1"><i><font color="Green" title="E32">A1</font></i></a>, <a class="ref" href="anproj_1.html#D8" title="ANPROJ_1:def.8">ANPROJ_1:def 8</a></i>;<br/>
<b>hence </b><a NAME="E6:61_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="vectsp10.html#E3:61_1_1"><i><font color="Green" title="E33">A2</font></i></a>, <a class="ref" href="hahnban1.html#D14" title="HAHNBAN1:def.14">HAHNBAN1:def 14</a></i>;<br/>


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