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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="rlvect_1.html#L2" title="RLVECT_1:struct.2">RLSStruct</a> ;<br/><b>let </b><font color="Maroon" title="c2">M</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">V</font>;<br/>



<b>assume </b><a NAME="E1:28"/><i><font color="Green" title="E18">A1</font></i>: 
<font color="Maroon" title="c2">M</font> is <a href="rusub_4.html#V2" title="RUSUB_4:attr.2">Affine</a>
 ;<br/>

<b>let </b><font color="Maroon" title="c3">u</font>, <font color="Maroon" title="c4">v</font> be   <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="convex1.html#D2" target="_self" title="CONVEX1:def.2">CONVEX1:def 2</a><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><b>that </b><br/><a NAME="E2:28"/>
(  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c5">r</font> &amp; <font color="Maroon" title="c5">r</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 1 )
 <b>and </b><br/><a NAME="E3:28"/><i><font color="Green" title="E19">A2</font></i>: 
( <font color="Maroon" title="c3">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">M</font> &amp; <font color="Maroon" title="c4">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">M</font> )
 ;<br/>

<b>set </b><font color="Maroon" title="c6">p</font> = 1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c5">r</font>;<br/>
<a NAME="E4:28"/>
1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c5">r</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">r</font>
 
;<br/>
<b>hence </b><a NAME="E5:28"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c5">r</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">*</a> <font color="Maroon" title="c3">u</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c5">r</font></span>)</span> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">*</a> <font color="Maroon" title="c4">v</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">M</font>
 <b>by </b><i><a class="txt" href="convex1.html#E1:28"><i><font color="Green" title="E18">A1</font></i></a>, <a class="txt" href="convex1.html#E3:28"><i><font color="Green" title="E19">A2</font></i></a>, <a class="ref" href="rusub_4.html#D5" title="RUSUB_4:def.5">RUSUB_4:def 5</a></i>;<br/>


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