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<div><span class="kw">theorem </span><a NAME="T4"><span class="comment"><font color="firebrick">:: CONVEX3:4</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   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">V</font> holds <br/> ( <font color="Olive" title="b2">M</font> is  <a href="convex1.html#V1" title="CONVEX1:attr.1">convex</a>  iff <span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><a href="rlvect_2.html#K6" title="RLVECT_2:func.6">Sum</a> <font color="Olive" title="b3">L</font></span>)</span> where <font color="Olive" title="b3">L</font> is   <a href="convex2.html#NM2" title="CONVEX2:NM.2">Convex_Combination</a> of <font color="Olive" title="b2">M</font> : <font color="Olive" title="b3">L</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="convex3.html#K1" title="CONVEX3:func.1">ConvexComb</a> <font color="Olive" title="b1">V</font> </span> } </span>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">M</font> ) <span class="kw">by</span> <span class="lab"><a class="txt" href="convex3.html#E8"><span class="lab"><font color="Green" title="E3">Lm1</font></span></a>, <a class="txt" href="convex3.html#E10"><span class="lab"><font color="Green" title="E5">Lm3</font></span></a></span>;<br/></div></div>
