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<div>:: <span class="kw">deftheorem </span>   defines <a href="convex4.html#V2" title="CONVEX4:attr.2">convex</a> <a onclick="hs(this)" href="javascript:()">CONVEX4:def 23 : <br/></a><span> 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#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> holds <br/> ( <font color="Olive" title="b2">M</font> is  <a href="convex4.html#V2" title="CONVEX4:attr.2">convex</a>  iff  for <font color="Olive" title="b3">u</font>, <font color="Olive" title="b4">v</font> being   <a href="clvect_1.html#NM1" title="CLVECT_1:NM.1">VECTOR</a> of <font color="Olive" title="b1">V</font><br/>  for <font color="Olive" title="b5">z</font> being   <a href="xcmplx_0.html#NM1" title="XCMPLX_0:NM.1">Complex</a>  st  ex <font color="Olive" title="b6">r</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a> st <br/>( <font color="Olive" title="b5">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b6">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="b6">r</font> &amp; <font color="Olive" title="b6">r</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 1 ) &amp; <font color="Olive" title="b3">u</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">M</font> &amp; <font color="Olive" title="b4">v</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">M</font> holds <br/><span class="p1">(<span class="default"><font color="Olive" title="b5">z</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Olive" title="b3">u</font></span>)</span> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <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="b5">z</font></span>)</span> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Olive" title="b4">v</font></span>)</span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">M</font> );<br/></span></div>
