<?xml version="1.0"?>
<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E57">Th80</font></span>: <a NAME="T83"><span class="comment"><font color="firebrick">:: CONVEX4:83</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">V</font> being   <a href="clvect_1.html#NM2" title="CLVECT_1:NM.2">ComplexLinearSpace</a><br/>  for <font color="Olive" title="b2">v</font> being   <a href="clvect_1.html#NM1" title="CLVECT_1:NM.1">VECTOR</a> of <font color="Olive" title="b1">V</font><br/>  for <font color="Olive" title="b3">L</font> being    <a href="convex4.html#M1" title="CONVEX4:mode.1">C_Linear_Combination</a> of <font color="Olive" title="b1">V</font>  st <font color="Olive" title="b3">L</font> is  <a href="convex4.html#V3" title="CONVEX4:attr.3">convex</a>  &amp;  <a href="convex4.html#K1" title="CONVEX4:func.1">Carrier</a> <font color="Olive" title="b3">L</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Olive" title="b2">v</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> holds <br/>(  ex <font color="Olive" title="b4">r</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a> st <br/>( <font color="Olive" title="b4">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">L</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">v</font> &amp; <font color="Olive" title="b4">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 ) &amp;  <a href="convex4.html#K4" title="CONVEX4:func.4">Sum</a> <font color="Olive" title="b3">L</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">L</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">v</font></span>)</span> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Olive" title="b2">v</font> )</div></div>
