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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E48">Th54</font></span>: <a NAME="T55"><span class="comment"><font color="firebrick">:: CONVEX4:55</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="clvect_1.html#V2" title="CLVECT_1:attr.2">vector-distributive</a>   <a href="clvect_1.html#V3" title="CLVECT_1:attr.3">scalar-distributive</a>   <a href="clvect_1.html#V4" title="CLVECT_1:attr.4">scalar-associative</a>   <a href="clvect_1.html#V5" title="CLVECT_1:attr.5">scalar-unital</a>   <a href="clvect_1.html#L1" title="CLVECT_1:struct.1">CLSStruct</a> <br/>  for <font color="Olive" title="b2">M1</font>, <font color="Olive" title="b3">M2</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="b4">z</font> being   <a href="xcmplx_0.html#NM1" title="XCMPLX_0:NM.1">Complex</a> holds  <font color="Olive" title="b4">z</font> <a href="convex4.html#K19" title="CONVEX4:func.19">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">M1</font> <a href="rusub_4.html#K6" title="RUSUB_4:func.6">+</a> <font color="Olive" title="b3">M2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">z</font> <a href="convex4.html#K19" title="CONVEX4:func.19">*</a> <font color="Olive" title="b2">M1</font></span>)</span> <a href="rusub_4.html#K6" title="RUSUB_4:func.6">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">z</font> <a href="convex4.html#K19" title="CONVEX4:func.19">*</a> <font color="Olive" title="b3">M2</font></span>)</span></div></div>
