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<b>let </b><font color="Maroon">V</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="rlvect_1.html#L2">RLSStruct</a> ;<br/><b>let </b><font color="Maroon">M</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">V</font>, <font color="Maroon">N</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">V</font>;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:18"/><i><font color="Green">E25</font></i>: 
<font color="Maroon">M</font> is <a href="convex3.html#V1" target="_self">cone</a>
 <b>and </b><br/><a NAME="E2:18"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">N</font> is <a href="convex3.html#V1" target="_self">cone</a>
 ;<br/>

<b>let </b><font color="Maroon">r</font> be   <a href="real_1.html#NM1">Real</a>; <i><font color="Red">:: according to </font></i><a class="ref" href="convex3.html#D3" target="_self">CONVEX3:def 3</a><br/><b>let </b><font color="Maroon">v</font> be   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">V</font>;<br/>



<b>assume </b><a NAME="E3:18"/><i><font color="Green">E33</font></i>: 
( <font color="Maroon">r</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 &amp; <font color="Maroon">v</font> <a href="hidden.html#R2">in</a> <font color="Maroon">M</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">N</font> )
 ;<br/>

<a NAME="E4:18"/><b>then </b><i><font color="Green">E35</font></i>: 
( <font color="Maroon">v</font> <a href="hidden.html#R2">in</a> <font color="Maroon">M</font> &amp; <font color="Maroon">v</font> <a href="hidden.html#R2">in</a> <font color="Maroon">N</font> )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E5:18"/><b>then </b><i><font color="Green">E37</font></i>: 
<font color="Maroon">r</font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">v</font> <a href="hidden.html#R2">in</a> <font color="Maroon">M</font>
 
<b>by </b><i>, , </i>;<br/>
<a NAME="E6:18"/>
<font color="Maroon">r</font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">v</font> <a href="hidden.html#R2">in</a> <font color="Maroon">N</font>
 
<b>by </b><i>, , , </i>;<br/>
<b>hence </b><a NAME="E7:18"/>
<font color="Maroon">r</font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">v</font> <a href="hidden.html#R2">in</a> <font color="Maroon">M</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">N</font>
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>


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