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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="rlvect_1.html#NM2">RealLinearSpace</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">c<sub>1</sub></font>; <i><font color="Red">:: according to </font></i><a class="ref" href="convex1.html#D2" target="_self">CONVEX1:def 2</a><br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="real_1.html#NM1">Real</a>;<br/>





<a NAME="E1:16"/>
 <a href="rlsub_1.html#K2">(Omega).</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#G2">RLSStruct</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="struct_0.html#U2">Zero</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="rlvect_1.html#U1">add</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="rlvect_1.html#U2">Mult</a> of <font color="Maroon">c<sub>1</sub></font> #)
 
<b>by </b><i><a class="ref" href="rlsub_1.html#D4">RLSUB_1:def 4</a></i>;<br/>
<a NAME="E2:16"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="rlsub_1.html#K2">(Omega).</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 
;<br/>
<b>hence </b><a NAME="E3:16"/>
( 0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 1 &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="rusub_4.html#K3">Up</a> <span class="p1">(<span class="default"><a href="rlsub_1.html#K2">(Omega).</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="rusub_4.html#K3">Up</a> <span class="p1">(<span class="default"><a href="rlsub_1.html#K2">(Omega).</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> implies <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="rlvect_1.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="rusub_4.html#K3">Up</a> <span class="p1">(<span class="default"><a href="rlsub_1.html#K2">(Omega).</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> )
 <b>by </b><i><a class="ref" href="rusub_4.html#D6">RUSUB_4:def 6</a></i>;<br/>


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