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<b>let </b><font color="Maroon" title="c1">V</font> be   <a href="clvect_1.html#NM2" title="CLVECT_1:NM.2">ComplexLinearSpace</a>;<br/><b>let </b><font color="Maroon" title="c2">u</font>, <font color="Maroon" title="c3">v</font> be   <a href="clvect_1.html#NM1" title="CLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="convex4.html#D23" target="_self" title="CONVEX4:def.23">CONVEX4:def 23</a><br/>



<b>thus </b><a NAME="E1:89"/>
for <font color="Olive" title="b1">z</font> being  <a href="cfunct_1.html#NM1" title="CFUNCT_1:NM.1">Complex</a>  st  ex <font color="Olive" title="b2">r</font> being  <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> st <br/>( <font color="Olive" title="b1">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">r</font> &amp;  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <font color="Olive" title="b2">r</font> &amp; <font color="Olive" title="b2">r</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> 1 ) &amp; <font color="Maroon" title="c2">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="convex4.html#K17" title="CONVEX4:func.17">Up</a> <span class="p1">(<span class="default"><a href="convex4.html#K18" title="CONVEX4:func.18">(Omega).</a> <font color="Maroon" title="c1">V</font></span>)</span> &amp; <font color="Maroon" title="c3">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="convex4.html#K17" title="CONVEX4:func.17">Up</a> <span class="p1">(<span class="default"><a href="convex4.html#K18" title="CONVEX4:func.18">(Omega).</a> <font color="Maroon" title="c1">V</font></span>)</span> holds <br/><span class="p1">(<span class="default"><font color="Olive" title="b1">z</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c2">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="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Olive" title="b1">z</font></span>)</span> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c3">v</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="convex4.html#K17" title="CONVEX4:func.17">Up</a> <span class="p1">(<span class="default"><a href="convex4.html#K18" title="CONVEX4:func.18">(Omega).</a> <font color="Maroon" title="c1">V</font></span>)</span>
 ;<br/>


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