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<div class="add">

<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be   <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>;<br/>





<b>assume </b><a NAME="E1:89"/><i><font color="Green">E39</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> is <a href="jordan1.html#V1">convex</a> &amp; <font color="Maroon">c<sub>3</sub></font> is <a href="jordan1.html#V1">convex</a> )
 ;<br/>

<b>thus </b><a NAME="E2:89"/>
<font color="Maroon">c<sub>2</sub></font> <a href="mathmorp.html#K5" target="_self">(O)</a> <font color="Maroon">c<sub>3</sub></font> is <a href="jordan1.html#V1">convex</a>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="89_1"><b>proof </b></a><div class="add">

<a NAME="E1:89_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="mathmorp.html#K3" target="_self">(-)</a> <font color="Maroon">c<sub>3</sub></font> is <a href="jordan1.html#V1">convex</a>
 
<b>by </b><i><a class="txt" href="mathmorp.html#E1:89"><i><font color="Green">E39</font></i></a>, <a class="ref" href="mathmorp.html#T77" target="_self">Th77</a></i>;<br/>
<a NAME="E2:89_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="mathmorp.html#K3" target="_self">(-)</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="mathmorp.html#K4" target="_self">(+)</a> <font color="Maroon">c<sub>3</sub></font> is <a href="jordan1.html#V1">convex</a>
 
<b>by </b><i><a class="txt" href="mathmorp.html#E1:89"><i><font color="Green">E39</font></i></a>, <a class="ref" href="mathmorp.html#T77" target="_self">Th77</a></i>;<br/>
<b>hence </b><a NAME="E3:89_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="mathmorp.html#K5" target="_self">(O)</a> <font color="Maroon">c<sub>3</sub></font> is <a href="jordan1.html#V1">convex</a>
 ;<br/>


</div><b>end;</b></div>

<a NAME="E3:89"/>
<font color="Maroon">c<sub>2</sub></font> <a href="mathmorp.html#K4" target="_self">(+)</a> <font color="Maroon">c<sub>3</sub></font> is <a href="jordan1.html#V1">convex</a>
 
<b>by </b><i><a class="txt" href="mathmorp.html#E1:89"><i><font color="Green">E39</font></i></a>, <a class="ref" href="mathmorp.html#T77" target="_self">Th77</a></i>;<br/>
<a NAME="E4:89"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="mathmorp.html#K4" target="_self">(+)</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="mathmorp.html#K3" target="_self">(-)</a> <font color="Maroon">c<sub>3</sub></font> is <a href="jordan1.html#V1">convex</a>
 
<b>by </b><i><a class="txt" href="mathmorp.html#E1:89"><i><font color="Green">E39</font></i></a>, <a class="ref" href="mathmorp.html#T77" target="_self">Th77</a></i>;<br/>
<b>hence </b><a NAME="E5:89"/>
<font color="Maroon">c<sub>2</sub></font> <a href="mathmorp.html#K6" target="_self">(o)</a> <font color="Maroon">c<sub>3</sub></font> is <a href="jordan1.html#V1">convex</a>
 ;<br/>


</div>
