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<b>let </b><font color="Maroon" title="c1">V</font> be   <a href="rlvect_1.html#NM2" title="RLVECT_1:NM.2">RealLinearSpace</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">L</font> being   <a href="rlvect_2.html#M1" title="RLVECT_2:mode.1">Linear_Combination</a> of <font color="Maroon" title="c1">V</font>  st <font color="Olive" title="b1">L</font> is <a href="circled1.html#V1" title="CIRCLED1:attr.1">circled</a> holds <br/><font color="Olive" title="b1">L</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="rlvect_2.html#K4" title="RLVECT_2:func.4">ZeroLC</a> <font color="Maroon" title="c1">V</font></span><br/><b>let </b><font color="Maroon" title="c2">L</font> be    <a href="rlvect_2.html#M1" title="RLVECT_2:mode.1">Linear_Combination</a> of <font color="Maroon" title="c1">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="c2">L</font> is <a href="circled1.html#V1" title="CIRCLED1:attr.1">circled</a> implies <font color="Maroon" title="c2">L</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="rlvect_2.html#K4" title="RLVECT_2:func.4">ZeroLC</a> <font color="Maroon" title="c1">V</font> )</span><br/>



<b>assume </b><b>that </b><br/><a NAME="E1:25"/><i><font color="Green" title="E15">A1</font></i>: 
<font color="Maroon" title="c2">L</font> is <a href="circled1.html#V1" title="CIRCLED1:attr.1">circled</a>
 <b>and </b><br/><a NAME="E2:25"/><i><font color="Green" title="E16">A2</font></i>: 
<font color="Maroon" title="c2">L</font> <a href="rlvect_2.html#R1" title="RLVECT_2:pred.1">=</a>  <a href="rlvect_2.html#K4" title="RLVECT_2:func.4">ZeroLC</a> <font color="Maroon" title="c1">V</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E3:25"/>
 <a href="rlvect_2.html#K3" title="RLVECT_2:func.3">Carrier</a> <font color="Maroon" title="c2">L</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<b>by </b><i><a class="txt" href="circled1.html#E1:25"><i><font color="Green" title="E15">A1</font></i></a>, <a class="ref" href="circled1.html#T16" target="_self" title="CIRCLED1:th.16">Th16</a></i>;<br/>
<b>hence </b><a NAME="E4:25"/>
contradiction
 <b>by </b><i><a class="txt" href="circled1.html#E2:25"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="rlvect_2.html#D7" title="RLVECT_2:def.7">RLVECT_2:def 7</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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