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<div><span class="kw">theorem </span><a NAME="T49"><span class="comment"><font color="firebrick">:: CONVEX4:49</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">V</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="rlvect_1.html#V2" title="RLVECT_1:attr.2">Abelian</a>   <a href="clvect_1.html#L1" title="CLVECT_1:struct.1">CLSStruct</a> <br/>  for <font color="Olive" title="b2">M</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">V</font>  st <font color="Olive" title="b2">M</font> is  <a href="convex4.html#V2" title="CONVEX4:attr.2">convex</a>  holds <br/> for <font color="Olive" title="b3">z</font> being   <a href="xcmplx_0.html#NM1" title="XCMPLX_0:NM.1">Complex</a>  st  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="b3">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">r</font> &amp;  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b4">r</font> &amp; <font color="Olive" title="b4">r</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 1 ) holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K6" title="COMPLEX1:func.6">1r</a> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Olive" title="b3">z</font></span>)</span> <a href="convex4.html#K19" title="CONVEX4:func.19">*</a> <font color="Olive" title="b2">M</font></span>)</span> <a href="rusub_4.html#K7" title="RUSUB_4:func.7">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">z</font> <a href="convex4.html#K19" title="CONVEX4:func.19">*</a> <font color="Olive" title="b2">M</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">M</font></div></div>
