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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="rlvect_1.html#NM2">RealLinearSpace</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be  non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be   <a href="convex2.html#NM2">Convex_Combination</a> of <font color="Maroon">c<sub>2</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>5</sub></font> be   <a href="real_1.html#NM1">Real</a>;<br/>







<b>assume </b><a NAME="E1:23"/><i><font color="Green">E12</font></i>: 
( 0 <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="xxreal_0.html#R1">&lt;</a> 1 )
 ;<br/>

<a NAME="E2:23"/><i><font color="Green">E13</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="rlvect_2.html#K8">*</a> <font color="Maroon">c<sub>3</sub></font> is    <a href="rlvect_2.html#M2">Linear_Combination</a> of <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="rlvect_2.html#T67">RLVECT_2:67</a></i>;<br/>
<a NAME="E3:23"/>
<span class="p1">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="rlvect_2.html#K8">*</a> <font color="Maroon">c<sub>4</sub></font> is    <a href="rlvect_2.html#M2">Linear_Combination</a> of <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="rlvect_2.html#T67">RLVECT_2:67</a></i>;<br/>
<b>hence </b><a NAME="E4:23"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="rlvect_2.html#K8">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="rlvect_2.html#K7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="rlvect_2.html#K8">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> is   <a href="convex2.html#NM2">Convex_Combination</a> of <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="convex2.html#E1:23"><i><font color="Green">E12</font></i></a>, <a class="txt" href="convex2.html#E2:23"><i><font color="Green">E13</font></i></a>, <a class="ref" href="convex2.html#T9" target="_self">Th9</a>, <a class="ref" href="rlvect_2.html#T59">RLVECT_2:59</a></i>;<br/>


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