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<span class="kw">let </span><font color="Maroon" title="c1">V</font> be   <a href="clvect_1.html#NM2" title="CLVECT_1:NM.2">ComplexLinearSpace</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">L</font> being   <a href="convex4.html#M1" title="CONVEX4:mode.1">C_Linear_Combination</a> of <font color="Maroon" title="c1">V</font>  st <font color="Olive" title="b1">L</font> is  <a href="convex4.html#V3" title="CONVEX4:attr.3">convex</a>  holds <br/><font color="Olive" title="b1">L</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="convex4.html#K2" title="CONVEX4:func.2">ZeroCLC</a> <font color="Maroon" title="c1">V</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">L</font> be    <a href="convex4.html#M1" title="CONVEX4:mode.1">C_Linear_Combination</a> of <font color="Maroon" title="c1">V</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">L</font> is  <a href="convex4.html#V3" title="CONVEX4:attr.3">convex</a>  implies <font color="Maroon" title="c2">L</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="convex4.html#K2" title="CONVEX4:func.2">ZeroCLC</a> <font color="Maroon" title="c1">V</font> )</span><br/>



<span class="kw">assume </span><a NAME="E1:116"/>
<font color="Maroon" title="c2">L</font> is  <a href="convex4.html#V3" title="CONVEX4:attr.3">convex</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">L</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="convex4.html#K2" title="CONVEX4:func.2">ZeroCLC</a> <font color="Maroon" title="c1">V</font></span><br/>

<a NAME="E2:116"/><span class="kw">then </span><span class="lab"><font color="Green" title="E62">A1</font></span>: 
 <a href="convex4.html#K1" title="CONVEX4:func.1">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> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="convex4.html#T80" target="_self" title="CONVEX4:th.80">Th80</a></span>;<br/>
<span class="kw">assume </span><a NAME="E3:116"/>
<font color="Maroon" title="c2">L</font> <a href="convex4.html#R1" title="CONVEX4:pred.1">=</a>  <a href="convex4.html#K2" title="CONVEX4:func.2">ZeroCLC</a> <font color="Maroon" title="c1">V</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<span class="kw">hence </span><a NAME="E4:116"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:116"><span class="lab"><font color="Green" title="E62">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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