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<div><span class="kw">theorem </span><a NAME="T13"><span class="comment"><font color="firebrick">:: CONVEX1:13</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">V</font> being   <a href="rlvect_1.html#NM2" title="RLVECT_1:NM.2">RealLinearSpace</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><br/>  for <font color="Olive" title="b3">r1</font>, <font color="Olive" title="b4">r2</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a>  st <font color="Olive" title="b3">r1</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <font color="Olive" title="b4">r2</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <font color="Olive" title="b2">M</font> is  <a href="convex1.html#V1" title="CONVEX1:attr.1">convex</a>  holds <br/><span class="p1">(<span class="default"><font color="Olive" title="b3">r1</font> <a href="convex1.html#K1" title="CONVEX1:func.1">*</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="b4">r2</font> <a href="convex1.html#K1" title="CONVEX1:func.1">*</a> <font color="Olive" title="b2">M</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">r1</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Olive" title="b4">r2</font></span>)</span> <a href="convex1.html#K1" title="CONVEX1:func.1">*</a> <font color="Olive" title="b2">M</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="convex1.html#E24"><span class="lab"><font color="Green" title="E15">Lm10</font></span></a>, <a class="ref" href="convex1.html#T12" target="_self" onmouseover="rs('convex1/T12')" onmouseout="rh()">Th12</a></span>;<br/></div></div>
