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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   <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="real_1.html#NM1">Real</a>;<br/>





<b>assume </b><a NAME="E1:25"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 &amp; <font color="Maroon">c<sub>4</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 &amp; <font color="Maroon">c<sub>2</sub></font> is <a href="convex1.html#V1" target="_self">convex</a> )
 ;<br/>

<b>hence </b><a NAME="E2:25"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="convex1.html#K1" target="_self">*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="rusub_4.html#K7">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="convex1.html#K1" target="_self">*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="real_1.html#K3">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="convex1.html#K1" target="_self">*</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="convex1.html#E24"><i><font color="Green">Lemma15</font></i></a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><br/>

<b>thus </b><a NAME="E3:25"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="real_1.html#K3">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="convex1.html#K1" target="_self">*</a> <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="convex1.html#K1" target="_self">*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="rusub_4.html#K7">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="convex1.html#K1" target="_self">*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="convex1.html#T12" target="_self">Th12</a></i>;<br/>


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