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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>;<br/><b>let </b><font color="Maroon" title="c2">M</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">V</font>;<br/><b>let </b><font color="Maroon" title="c3">L1</font>, <font color="Maroon" title="c4">L2</font> be   <a href="convex2.html#NM2" title="CONVEX2:NM.2">Convex_Combination</a> of <font color="Maroon" title="c2">M</font>;<br/><b>let </b><font color="Maroon" title="c5">r</font> be   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>;<br/>







<b>assume </b><a NAME="E1:23"/><i><font color="Green" title="E12">A1</font></i>: 
( 0 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <font color="Maroon" title="c5">r</font> &amp; <font color="Maroon" title="c5">r</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> 1 )
 ;<br/>

<a NAME="E2:23"/><i><font color="Green" title="E13">A2</font></i>: 
<font color="Maroon" title="c5">r</font> <a href="rlvect_2.html#K8" title="RLVECT_2:func.8">*</a> <font color="Maroon" title="c3">L1</font> is    <a href="rlvect_2.html#M2" title="RLVECT_2:mode.2">Linear_Combination</a> of <font color="Maroon" title="c2">M</font>
 
<b>by </b><i><a class="ref" href="rlvect_2.html#T67" title="RLVECT_2:th.67">RLVECT_2:67</a></i>;<br/>
<a NAME="E3:23"/>
<span class="p1">(<span class="default">1 <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <font color="Maroon" title="c5">r</font></span>)</span> <a href="rlvect_2.html#K8" title="RLVECT_2:func.8">*</a> <font color="Maroon" title="c4">L2</font> is    <a href="rlvect_2.html#M2" title="RLVECT_2:mode.2">Linear_Combination</a> of <font color="Maroon" title="c2">M</font>
 
<b>by </b><i><a class="ref" href="rlvect_2.html#T67" title="RLVECT_2:th.67">RLVECT_2:67</a></i>;<br/>
<b>hence </b><a NAME="E4:23"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c5">r</font> <a href="rlvect_2.html#K8" title="RLVECT_2:func.8">*</a> <font color="Maroon" title="c3">L1</font></span>)</span> <a href="rlvect_2.html#K7" title="RLVECT_2:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <font color="Maroon" title="c5">r</font></span>)</span> <a href="rlvect_2.html#K8" title="RLVECT_2:func.8">*</a> <font color="Maroon" title="c4">L2</font></span>)</span> is   <a href="convex2.html#NM2" title="CONVEX2:NM.2">Convex_Combination</a> of <font color="Maroon" title="c2">M</font>
 <b>by </b><i><a class="txt" href="convex2.html#E1:23"><i><font color="Green" title="E12">A1</font></i></a>, <a class="txt" href="convex2.html#E2:23"><i><font color="Green" title="E13">A2</font></i></a>, <a class="ref" href="convex2.html#T9" target="_self" title="CONVEX2:th.9">Th9</a>, <a class="ref" href="rlvect_2.html#T59" title="RLVECT_2:th.59">RLVECT_2:59</a></i>;<br/>


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