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<span class="kw">let </span><font color="Maroon" title="c1">X</font> be   <a href="rlvect_1.html#NM2" title="RLVECT_1:NM.2">RealLinearSpace</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">M</font> being   <a href="rltopsp1.html#V3" title="RLTOPSP1:attr.3">circled</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font> holds   <a href="convex1.html#K3" title="CONVEX1:func.3">conv</a> <font color="Olive" title="b1">M</font> is  <a href="rltopsp1.html#V3" title="RLTOPSP1:attr.3">circled</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">M</font> be   <a href="rltopsp1.html#V3" title="RLTOPSP1:attr.3">circled</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="convex1.html#K3" title="CONVEX1:func.3">conv</a> <font color="Maroon" title="c2">M</font> is  <a href="rltopsp1.html#V3" title="RLTOPSP1:attr.3">circled</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c3">r</font> be   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="rltopsp1.html#D6" target="_self" title="RLTOPSP1:def.6">RLTOPSP1:def 6</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <font color="Maroon" title="c3">r</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 1 implies <font color="Maroon" title="c3">r</font> <a href="convex1.html#K1" title="CONVEX1:func.1">*</a> <span class="p1">(<span class="default"><a href="convex1.html#K3" title="CONVEX1:func.3">conv</a> <font color="Maroon" title="c2">M</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="convex1.html#K3" title="CONVEX1:func.3">conv</a> <font color="Maroon" title="c2">M</font> )</span><br/>





<span class="kw">assume </span><a NAME="E1:49"/>
 <a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <font color="Maroon" title="c3">r</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 1
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">r</font> <a href="convex1.html#K1" title="CONVEX1:func.1">*</a> <span class="p1">(<span class="default"><a href="convex1.html#K3" title="CONVEX1:func.3">conv</a> <font color="Maroon" title="c2">M</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="convex1.html#K3" title="CONVEX1:func.3">conv</a> <font color="Maroon" title="c2">M</font></span><br/>

<a NAME="E2:49"/><span class="kw">then </span><span class="lab"><font color="Green" title="E33">A1</font></span>: 
<font color="Maroon" title="c3">r</font> <a href="convex1.html#K1" title="CONVEX1:func.1">*</a> <font color="Maroon" title="c2">M</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">M</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="rltopsp1.html#D6" target="_self" title="RLTOPSP1:def.6">Def6</a></span>;<br/>
<a NAME="E3:49"/>
<font color="Maroon" title="c3">r</font> <a href="convex1.html#K1" title="CONVEX1:func.1">*</a> <span class="p1">(<span class="default"><a href="convex1.html#K3" title="CONVEX1:func.3">conv</a> <font color="Maroon" title="c2">M</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="convex1.html#K3" title="CONVEX1:func.3">conv</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">r</font> <a href="convex1.html#K1" title="CONVEX1:func.1">*</a> <font color="Maroon" title="c2">M</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="rltopsp1.html#T18" target="_self" title="RLTOPSP1:th.18">Th19</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:49"/>
<font color="Maroon" title="c3">r</font> <a href="convex1.html#K1" title="CONVEX1:func.1">*</a> <span class="p1">(<span class="default"><a href="convex1.html#K3" title="CONVEX1:func.3">conv</a> <font color="Maroon" title="c2">M</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="convex1.html#K3" title="CONVEX1:func.3">conv</a> <font color="Maroon" title="c2">M</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:49"><span class="lab"><font color="Green" title="E33">A1</font></span></a>, <a class="ref" href="rltopsp1.html#T20" target="_self" title="RLTOPSP1:th.20">Th21</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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