<?xml version="1.0"?>
<div class="add">

<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">L1</font>, <font color="Olive" title="b2">L2</font> being   <a href="convex4.html#M1" title="CONVEX4:mode.1">C_Linear_Combination</a> of <font color="Maroon" title="c1">V</font> holds  <span class="p1">(<span class="default"><a href="rlvect_2.html#K1" title="RLVECT_2:func.1">vector</a> <span class="p2">(<span class="default"><a href="convex4.html#K15" title="CONVEX4:func.15">LC_CLSpace</a> <font color="Maroon" title="c1">V</font></span>)</span>,<font color="Olive" title="b1">L1</font></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p1">(<span class="default"><a href="rlvect_2.html#K1" title="RLVECT_2:func.1">vector</a> <span class="p2">(<span class="default"><a href="convex4.html#K15" title="CONVEX4:func.15">LC_CLSpace</a> <font color="Maroon" title="c1">V</font></span>)</span>,<font color="Olive" title="b2">L2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">L1</font> <a href="convex4.html#K9" title="CONVEX4:func.9">-</a> <font color="Olive" title="b2">L2</font></span><br/><b>let </b><font color="Maroon" title="c2">L1</font>, <font color="Maroon" title="c3">L2</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"> <span class="p1">(<span class="default"><a href="rlvect_2.html#K1" title="RLVECT_2:func.1">vector</a> <span class="p2">(<span class="default"><a href="convex4.html#K15" title="CONVEX4:func.15">LC_CLSpace</a> <font color="Maroon" title="c1">V</font></span>)</span>,<font color="Maroon" title="c2">L1</font></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p1">(<span class="default"><a href="rlvect_2.html#K1" title="RLVECT_2:func.1">vector</a> <span class="p2">(<span class="default"><a href="convex4.html#K15" title="CONVEX4:func.15">LC_CLSpace</a> <font color="Maroon" title="c1">V</font></span>)</span>,<font color="Maroon" title="c3">L2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">L1</font> <a href="convex4.html#K9" title="CONVEX4:func.9">-</a> <font color="Maroon" title="c3">L2</font></span><br/>





<a NAME="E1:62"/>
(  <a href="convex4.html#K8" title="CONVEX4:func.8">-</a> <font color="Maroon" title="c3">L2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="convex4.html#K10" title="CONVEX4:func.10">C_LinComb</a> <font color="Maroon" title="c1">V</font> &amp; the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="convex4.html#K15" title="CONVEX4:func.15">LC_CLSpace</a> <font color="Maroon" title="c1">V</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="convex4.html#K10" title="CONVEX4:func.10">C_LinComb</a> <font color="Maroon" title="c1">V</font> )
 
<b>by </b><i><a class="ref" href="convex4.html#D12" target="_self" title="CONVEX4:def.12">Def8</a></i>;<br/>
<a NAME="E2:62"/><b>then </b><i><font color="Green" title="E40">A1</font></i>: 
 <a href="convex4.html#K8" title="CONVEX4:func.8">-</a> <font color="Maroon" title="c3">L2</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a>  <a href="convex4.html#K15" title="CONVEX4:func.15">LC_CLSpace</a> <font color="Maroon" title="c1">V</font>
 
<b>by </b><i><a class="ref" href="struct_0.html#D5" title="STRUCT_0:def.5">STRUCT_0:def 5</a></i>;<br/>
 <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p1">(<span class="default"><a href="rlvect_2.html#K1" title="RLVECT_2:func.1">vector</a> <span class="p2">(<span class="default"><a href="convex4.html#K15" title="CONVEX4:func.15">LC_CLSpace</a> <font color="Maroon" title="c1">V</font></span>)</span>,<font color="Maroon" title="c3">L2</font></span>)</span> = 
 <a href="convex4.html#K8" title="CONVEX4:func.8">-</a> <font color="Maroon" title="c3">L2</font>
<b>by </b><i><a class="ref" href="convex4.html#T40" target="_self" title="CONVEX4:th.40">Th98</a></i>
<br/>.= 
 <a href="rlvect_2.html#K1" title="RLVECT_2:func.1">vector</a> <span class="p1">(<span class="default"><a href="convex4.html#K15" title="CONVEX4:func.15">LC_CLSpace</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="convex4.html#K8" title="CONVEX4:func.8">-</a> <font color="Maroon" title="c3">L2</font></span>)</span>
<b>by </b><i><a class="txt" href="#E2:62"><i><font color="Green" title="E40">A1</font></i></a>, <a class="ref" href="rlvect_2.html#D1" title="RLVECT_2:def.1">RLVECT_2:def 1</a></i>
;<br/>
<b>hence </b><a NAME="E4:62"/>
<span class="p1">(<span class="default"><a href="rlvect_2.html#K1" title="RLVECT_2:func.1">vector</a> <span class="p2">(<span class="default"><a href="convex4.html#K15" title="CONVEX4:func.15">LC_CLSpace</a> <font color="Maroon" title="c1">V</font></span>)</span>,<font color="Maroon" title="c2">L1</font></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p1">(<span class="default"><a href="rlvect_2.html#K1" title="RLVECT_2:func.1">vector</a> <span class="p2">(<span class="default"><a href="convex4.html#K15" title="CONVEX4:func.15">LC_CLSpace</a> <font color="Maroon" title="c1">V</font></span>)</span>,<font color="Maroon" title="c3">L2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">L1</font> <a href="convex4.html#K9" title="CONVEX4:func.9">-</a> <font color="Maroon" title="c3">L2</font>
 <b>by </b><i><a class="ref" href="convex4.html#T38" target="_self" title="CONVEX4:th.38">Th96</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>
