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

<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>, <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</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>5</sub></font>, <font color="Maroon">c<sub>6</sub></font>, <font color="Maroon">c<sub>7</sub></font> be   <a href="real_1.html#NM1">Real</a>;<br/>





<b>assume </b><b>that </b><br/><a NAME="E1:7"/><i><font color="Green">E6</font></i>: 
<font color="Maroon">c<sub>2</sub></font> is <a href="rltopsp1.html#V3">circled</a>
 <b>and </b><br/><a NAME="E2:7"/><i><font color="Green">E7</font></i>: 
<font color="Maroon">c<sub>3</sub></font> is <a href="rltopsp1.html#V3">circled</a>
 <b>and </b><br/><a NAME="E3:7"/><i><font color="Green">E8</font></i>: 
<font color="Maroon">c<sub>4</sub></font> is <a href="rltopsp1.html#V3">circled</a>
 ;<br/>

<a NAME="E4:7"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="convex1.html#K1">*</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>6</sub></font> <a href="convex1.html#K1">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> is <a href="rltopsp1.html#V3">circled</a>
 
<b>by </b><i><a class="txt" href="circled1.html#E1:7"><i><font color="Green">E6</font></i></a>, <a class="txt" href="circled1.html#E2:7"><i><font color="Green">E7</font></i></a>, <a class="ref" href="circled1.html#T3" target="_self">Th3</a></i>;<br/>
<a NAME="E5:7"/><b>then </b>
<span class="p1">(<span class="default">1 <a href="convex1.html#K1">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="convex1.html#K1">*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="rusub_4.html#K7">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="convex1.html#K1">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <a href="rusub_4.html#K7">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="convex1.html#K1">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> is <a href="rltopsp1.html#V3">circled</a>
 
<b>by </b><i><a class="txt" href="circled1.html#E3:7"><i><font color="Green">E8</font></i></a>, <a class="ref" href="circled1.html#T3" target="_self">Th3</a></i>;<br/>
<b>hence </b><a NAME="E6:7"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="convex1.html#K1">*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="rusub_4.html#K7">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="convex1.html#K1">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="rusub_4.html#K7">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="convex1.html#K1">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> is <a href="rltopsp1.html#V3">circled</a>
 <b>by </b><i><a class="ref" href="convex1.html#T32">CONVEX1:32</a></i>;<br/>


</div>
