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<b>let </b><font color="Maroon" title="c1">V</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="clvect_1.html#L1" title="CLVECT_1:struct.1">CLSStruct</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">A</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">V</font><br/> for <font color="Olive" title="b2">a</font> being  <a href="cfunct_1.html#NM1" title="CFUNCT_1:NM.1">Complex</a><br/> for <font color="Olive" title="b3">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="b3">L</font> is    <a href="convex4.html#M2" title="CONVEX4:mode.2">C_Linear_Combination</a> of <font color="Olive" title="b1">A</font> holds <br/><font color="Olive" title="b2">a</font> <a href="convex4.html#K7" title="CONVEX4:func.7">*</a> <font color="Olive" title="b3">L</font> is    <a href="convex4.html#M2" title="CONVEX4:mode.2">C_Linear_Combination</a> of <font color="Olive" title="b1">A</font></span><br/><b>let </b><font color="Maroon" title="c2">A</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</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"> for <font color="Olive" title="b1">a</font> being  <a href="cfunct_1.html#NM1" title="CFUNCT_1:NM.1">Complex</a><br/> for <font color="Olive" title="b2">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="b2">L</font> is    <a href="convex4.html#M2" title="CONVEX4:mode.2">C_Linear_Combination</a> of <font color="Maroon" title="c2">A</font> holds <br/><font color="Olive" title="b1">a</font> <a href="convex4.html#K7" title="CONVEX4:func.7">*</a> <font color="Olive" title="b2">L</font> is    <a href="convex4.html#M2" title="CONVEX4:mode.2">C_Linear_Combination</a> of <font color="Maroon" title="c2">A</font></span><br/><b>let </b><font color="Maroon" title="c3">a</font> be   <a href="cfunct_1.html#NM1" title="CFUNCT_1:NM.1">Complex</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="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#M2" title="CONVEX4:mode.2">C_Linear_Combination</a> of <font color="Maroon" title="c2">A</font> holds <br/><font color="Maroon" title="c3">a</font> <a href="convex4.html#K7" title="CONVEX4:func.7">*</a> <font color="Olive" title="b1">L</font> is    <a href="convex4.html#M2" title="CONVEX4:mode.2">C_Linear_Combination</a> of <font color="Maroon" title="c2">A</font></span><br/><b>let </b><font color="Maroon" title="c4">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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c4">L</font> is    <a href="convex4.html#M2" title="CONVEX4:mode.2">C_Linear_Combination</a> of <font color="Maroon" title="c2">A</font> implies <font color="Maroon" title="c3">a</font> <a href="convex4.html#K7" title="CONVEX4:func.7">*</a> <font color="Maroon" title="c4">L</font> is    <a href="convex4.html#M2" title="CONVEX4:mode.2">C_Linear_Combination</a> of <font color="Maroon" title="c2">A</font> )</span><br/>







<b>assume </b><a NAME="E1:37"/><i><font color="Green" title="E27">A1</font></i>: 
<font color="Maroon" title="c4">L</font> is    <a href="convex4.html#M2" title="CONVEX4:mode.2">C_Linear_Combination</a> of <font color="Maroon" title="c2">A</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">a</font> <a href="convex4.html#K7" title="CONVEX4:func.7">*</a> <font color="Maroon" title="c4">L</font> is    <a href="convex4.html#M2" title="CONVEX4:mode.2">C_Linear_Combination</a> of <font color="Maroon" title="c2">A</font></span><br/>

<a NAME="E2:37"/><i><font color="Green" title="E28">A2</font></i>: 
( <font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="complex1.html#K5" title="COMPLEX1:func.5">0c</a>  implies <font color="Maroon" title="c3">a</font> <a href="convex4.html#K7" title="CONVEX4:func.7">*</a> <font color="Maroon" title="c4">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> )
 
<b>by </b><i><a class="ref" href="convex4.html#T25" target="_self" title="CONVEX4:th.25">Th66</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:37_1"/>
<font color="Maroon" title="c3">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="complex1.html#K5" title="COMPLEX1:func.5">0c</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">a</font> <a href="convex4.html#K7" title="CONVEX4:func.7">*</a> <font color="Maroon" title="c4">L</font> is    <a href="convex4.html#M2" title="CONVEX4:mode.2">C_Linear_Combination</a> of <font color="Maroon" title="c2">A</font></span><br/><a NAME="E2:37_1"/><b>then </b>
(  <a href="convex4.html#K1" title="CONVEX4:func.1">Carrier</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="convex4.html#K7" title="CONVEX4:func.7">*</a> <font color="Maroon" title="c4">L</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="convex4.html#K1" title="CONVEX4:func.1">Carrier</a> <font color="Maroon" title="c4">L</font> &amp;  <a href="convex4.html#K1" title="CONVEX4:func.1">Carrier</a> <font color="Maroon" title="c4">L</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">A</font> )
 <b>by </b><i><a class="txt" href="convex4.html#E1:37"><i><font color="Green" title="E27">A1</font></i></a>, <a class="ref" href="convex4.html#D4" target="_self" title="CONVEX4:def.4">Def3</a>, <a class="ref" href="convex4.html#T24" target="_self" title="CONVEX4:th.24">Th65</a></i>;<br/><b>hence </b><a NAME="E3:37_1"/>
<font color="Maroon" title="c3">a</font> <a href="convex4.html#K7" title="CONVEX4:func.7">*</a> <font color="Maroon" title="c4">L</font> is    <a href="convex4.html#M2" title="CONVEX4:mode.2">C_Linear_Combination</a> of <font color="Maroon" title="c2">A</font>
 <b>by </b><i><a class="ref" href="convex4.html#D4" target="_self" title="CONVEX4:def.4">Def3</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:37"/>
<font color="Maroon" title="c3">a</font> <a href="convex4.html#K7" title="CONVEX4:func.7">*</a> <font color="Maroon" title="c4">L</font> is    <a href="convex4.html#M2" title="CONVEX4:mode.2">C_Linear_Combination</a> of <font color="Maroon" title="c2">A</font>
 <b>by </b><i><a class="txt" href="convex4.html#E2:37"><i><font color="Green" title="E28">A2</font></i></a>, <a class="ref" href="convex4.html#T4" target="_self" title="CONVEX4:th.4">Th34</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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