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<b>let </b><font color="Maroon" title="c3">f</font> be   <a href="hahnban1.html#NM1" title="HAHNBAN1:NM.1">Functional</a> of <font color="Maroon" title="c2">V</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">f</font> is <a href="realset1.html#V1" title="REALSET1:attr.1">trivial</a> implies <font color="Maroon" title="c3">f</font> is <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</a> )</span><br/>

<b>assume </b><a NAME="E1:54_1_1"/><i><font color="Green" title="E28">A1</font></i>: 
<font color="Maroon" title="c3">f</font> is <a href="realset1.html#V1" title="REALSET1:attr.1">trivial</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">f</font> is <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</a></span><br/>

<b>assume </b><a NAME="E2:54_1_1"/>
not <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/>

<b>then reconsider </b><font color="Maroon" title="c4">f</font> = <font color="Maroon" title="c3">f</font> as  non <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</a> <a href="hahnban1.html#NM1" title="HAHNBAN1:NM.1">Functional</a> of <font color="Maroon" title="c2">V</font> ;<br/>
<a NAME="E4:54_1_1"/>
not <font color="Maroon" title="c4">f</font> is <a href="realset1.html#V1" title="REALSET1:attr.1">trivial</a>
 
;<br/>
<b>hence </b><a NAME="E5:54_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="vectsp10.html#E1:54_1_1"><i><font color="Green" title="E28">A1</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/>


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