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<div><span class="kw">theorem </span><a NAME="T6"><span class="comment"><font color="firebrick">:: CONVEX1:6</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="rlvect_1.html#V3" title="RLVECT_1:attr.3">add-associative</a>   <a href="rlvect_1.html#V5" title="RLVECT_1:attr.5">vector-distributive</a>   <a href="rlvect_1.html#V6" title="RLVECT_1:attr.6">scalar-distributive</a>   <a href="rlvect_1.html#V7" title="RLVECT_1:attr.7">scalar-associative</a>   <a href="rlvect_1.html#V8" title="RLVECT_1:attr.8">scalar-unital</a>   <a href="rlvect_1.html#L1" title="RLVECT_1:struct.1">RLSStruct</a> <br/>  for <font color="Olive" title="b2">M</font>, <font color="Olive" title="b3">N</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="convex1.html#V1" title="CONVEX1:attr.1">convex</a>  &amp; <font color="Olive" title="b3">N</font> is  <a href="convex1.html#V1" title="CONVEX1:attr.1">convex</a>  holds <br/> for <font color="Olive" title="b4">r</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a> holds  <span class="p1">(<span class="default"><font color="Olive" title="b4">r</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"><span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Olive" title="b4">r</font></span>)</span> <a href="convex1.html#K1" title="CONVEX1:func.1">*</a> <font color="Olive" title="b3">N</font></span>)</span> is  <a href="convex1.html#V1" title="CONVEX1:attr.1">convex</a> </div></div>
