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<b>set </b><font color="Maroon" title="c2">S</font> =  <a href="clvect_1.html#G1" title="CLVECT_1:aggr.1">CLSStruct</a>(# <span class="p1">(<span class="default"><a href="convex4.html#K10" title="CONVEX4:func.10">C_LinComb</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="convex4.html#K12" title="CONVEX4:func.12">@</a> <span class="p2">(<span class="default"><a href="convex4.html#K2" title="CONVEX4:func.2">ZeroCLC</a> <font color="Maroon" title="c1">V</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="convex4.html#K13" title="CONVEX4:func.13">C_LCAdd</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="convex4.html#K14" title="CONVEX4:func.14">C_LCMult</a> <font color="Maroon" title="c1">V</font></span>)</span> #);<br/>
<div><i><font color="Green" title="E37">X0</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="57_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c3">a</font>, <font color="Maroon" title="c4">b</font> be   <a href="cfunct_1.html#NM1" title="CFUNCT_1:NM.1">Complex</a>;<br/><b>let </b><font color="Maroon" title="c5">v</font>, <font color="Maroon" title="c6">u</font>, <font color="Maroon" title="c7">w</font> be   <a href="clvect_1.html#NM1" title="CLVECT_1:NM.1">VECTOR</a> of <a href="clvect_1.html#G1" title="CLVECT_1:aggr.1">CLSStruct</a>(# <span class="p1">(<span class="default"><a href="convex4.html#K10" title="CONVEX4:func.10">C_LinComb</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="convex4.html#K12" title="CONVEX4:func.12">@</a> <span class="p2">(<span class="default"><a href="convex4.html#K2" title="CONVEX4:func.2">ZeroCLC</a> <font color="Maroon" title="c1">V</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="convex4.html#K13" title="CONVEX4:func.13">C_LCAdd</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="convex4.html#K14" title="CONVEX4:func.14">C_LCMult</a> <font color="Maroon" title="c1">V</font></span>)</span> #);<br/><b>reconsider </b><font color="Maroon" title="c8">x</font> = <font color="Maroon" title="c5">v</font>, <font color="Maroon" title="c9">y</font> = <font color="Maroon" title="c6">u</font>, <font color="Maroon" title="c10">z</font> = <font color="Maroon" title="c7">w</font>, <font color="Maroon" title="c11">yx</font> = <font color="Maroon" title="c6">u</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c5">v</font>, <font color="Maroon" title="c12">xz</font> = <font color="Maroon" title="c5">v</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c7">w</font>, <font color="Maroon" title="c13">ax</font> = <font color="Maroon" title="c3">a</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c5">v</font>, <font color="Maroon" title="c14">az</font> = <font color="Maroon" title="c3">a</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c7">w</font>, <font color="Maroon" title="c15">bx</font> = <font color="Maroon" title="c4">b</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c5">v</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="convex4.html#K10" title="CONVEX4:func.10">C_LinComb</a> <font color="Maroon" title="c1">V</font> ;<br/><a NAME="E2:57_1_1_1"/>
(  <a href="convex4.html#K11" title="CONVEX4:func.11">@</a> <font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">v</font> &amp;  <a href="convex4.html#K11" title="CONVEX4:func.11">@</a> <font color="Maroon" title="c9">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">u</font> &amp;  <a href="convex4.html#K11" title="CONVEX4:func.11">@</a> <font color="Maroon" title="c10">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">w</font> &amp;  <a href="convex4.html#K11" title="CONVEX4:func.11">@</a> <font color="Maroon" title="c11">yx</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">u</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c5">v</font> &amp;  <a href="convex4.html#K11" title="CONVEX4:func.11">@</a> <font color="Maroon" title="c12">xz</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">v</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c7">w</font> &amp;  <a href="convex4.html#K11" title="CONVEX4:func.11">@</a> <font color="Maroon" title="c13">ax</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c5">v</font> &amp;  <a href="convex4.html#K11" title="CONVEX4:func.11">@</a> <font color="Maroon" title="c14">az</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c7">w</font> &amp;  <a href="convex4.html#K11" title="CONVEX4:func.11">@</a> <font color="Maroon" title="c15">bx</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c5">v</font> )
 ;<br/><b>then reconsider </b><font color="Maroon" title="c16">K</font> = <font color="Maroon" title="c5">v</font>, <font color="Maroon" title="c17">L</font> = <font color="Maroon" title="c6">u</font>, <font color="Maroon" title="c18">M</font> = <font color="Maroon" title="c7">w</font>, <font color="Maroon" title="c19">LK</font> = <font color="Maroon" title="c6">u</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c5">v</font>, <font color="Maroon" title="c20">KM</font> = <font color="Maroon" title="c5">v</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c7">w</font>, <font color="Maroon" title="c21">aK</font> = <font color="Maroon" title="c3">a</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c5">v</font>, <font color="Maroon" title="c22">aM</font> = <font color="Maroon" title="c3">a</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c7">w</font>, <font color="Maroon" title="c23">bK</font> = <font color="Maroon" title="c4">b</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c5">v</font> as    <a href="convex4.html#M1" title="CONVEX4:mode.1">C_Linear_Combination</a> of <font color="Maroon" title="c1">V</font> ;<br/><div><i><font color="Green" title="E38">A1</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="57_1_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c24">v</font>, <font color="Maroon" title="c25">u</font> be   <a href="clvect_1.html#NM1" title="CLVECT_1:NM.1">VECTOR</a> of <a href="clvect_1.html#G1" title="CLVECT_1:aggr.1">CLSStruct</a>(# <span class="p1">(<span class="default"><a href="convex4.html#K10" title="CONVEX4:func.10">C_LinComb</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="convex4.html#K12" title="CONVEX4:func.12">@</a> <span class="p2">(<span class="default"><a href="convex4.html#K2" title="CONVEX4:func.2">ZeroCLC</a> <font color="Maroon" title="c1">V</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="convex4.html#K13" title="CONVEX4:func.13">C_LCAdd</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="convex4.html#K14" title="CONVEX4:func.14">C_LCMult</a> <font color="Maroon" title="c1">V</font></span>)</span> #);<br/><b>let </b><font color="Maroon" title="c26">K</font>, <font color="Maroon" title="c27">L</font> be    <a href="convex4.html#M1" title="CONVEX4:mode.1">C_Linear_Combination</a> of <font color="Maroon" title="c1">V</font>;<br/><b>assume </b><a NAME="E1:57_1_1_1_1"/><i><font color="Green" title="E39">A2</font></i>: 
( <font color="Maroon" title="c24">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c26">K</font> &amp; <font color="Maroon" title="c25">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c27">L</font> )
 ;<br/><a NAME="E2:57_1_1_1_1"/>
(  <a href="convex4.html#K11" title="CONVEX4:func.11">@</a> <span class="p1">(<span class="default"><a href="convex4.html#K12" title="CONVEX4:func.12">@</a> <font color="Maroon" title="c26">K</font></span>)</span> <a href="convex4.html#R1" title="CONVEX4:pred.1">=</a> <font color="Maroon" title="c26">K</font> &amp;  <a href="convex4.html#K11" title="CONVEX4:func.11">@</a> <span class="p1">(<span class="default"><a href="convex4.html#K12" title="CONVEX4:func.12">@</a> <font color="Maroon" title="c27">L</font></span>)</span> <a href="convex4.html#R1" title="CONVEX4:pred.1">=</a> <font color="Maroon" title="c27">L</font> )
 ;<br/><b>hence </b><a NAME="E3:57_1_1_1_1"/>
<font color="Maroon" title="c24">v</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c25">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c26">K</font> <a href="convex4.html#K5" title="CONVEX4:func.5">+</a> <font color="Maroon" title="c27">L</font>
 <b>by </b><i><a class="txt" href="convex4.html#E1:57_1_1_1_1"><i><font color="Green" title="E39">A2</font></i></a>, <a class="ref" href="convex4.html#D15" target="_self" title="CONVEX4:def.15">Def9</a></i>;<br/></div><b>end;</b></div><div><i><font color="Green" title="E39">A4</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="57_1_1_1_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c24">v</font> be   <a href="clvect_1.html#NM1" title="CLVECT_1:NM.1">VECTOR</a> of <a href="clvect_1.html#G1" title="CLVECT_1:aggr.1">CLSStruct</a>(# <span class="p1">(<span class="default"><a href="convex4.html#K10" title="CONVEX4:func.10">C_LinComb</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="convex4.html#K12" title="CONVEX4:func.12">@</a> <span class="p2">(<span class="default"><a href="convex4.html#K2" title="CONVEX4:func.2">ZeroCLC</a> <font color="Maroon" title="c1">V</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="convex4.html#K13" title="CONVEX4:func.13">C_LCAdd</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="convex4.html#K14" title="CONVEX4:func.14">C_LCMult</a> <font color="Maroon" title="c1">V</font></span>)</span> #);<br/><b>let </b><font color="Maroon" title="c25">L</font> be    <a href="convex4.html#M1" title="CONVEX4:mode.1">C_Linear_Combination</a> of <font color="Maroon" title="c1">V</font>;<br/><b>let </b><font color="Maroon" title="c26">a</font> be   <a href="cfunct_1.html#NM1" title="CFUNCT_1:NM.1">Complex</a>;<br/><b>assume </b><a NAME="E1:57_1_1_1_2"/>
<font color="Maroon" title="c24">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c25">L</font>
 ;<br/><a NAME="E2:57_1_1_1_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="convex4.html#K14" title="CONVEX4:func.14">C_LCMult</a> <font color="Maroon" title="c1">V</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c26">a</font>,<font color="Maroon" title="c24">v</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c26">a</font> <a href="convex4.html#K7" title="CONVEX4:func.7">*</a> <span class="p1">(<span class="default"><a href="convex4.html#K11" title="CONVEX4:func.11">@</a> <span class="p2">(<span class="default"><a href="convex4.html#K12" title="CONVEX4:func.12">@</a> <font color="Maroon" title="c25">L</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="convex4.html#D16" target="_self" title="CONVEX4:def.16">Def10</a></i>;<br/><b>hence </b><a NAME="E3:57_1_1_1_2"/>
<font color="Maroon" title="c26">a</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c24">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c26">a</font> <a href="convex4.html#K7" title="CONVEX4:func.7">*</a> <font color="Maroon" title="c25">L</font>
 ;<br/></div><b>end;</b></div><b>thus </b><font color="Maroon" title="c5">v</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c7">w</font> = 
<font color="Maroon" title="c16">K</font> <a href="convex4.html#K5" title="CONVEX4:func.5">+</a> <font color="Maroon" title="c18">M</font>
<b>by </b><i><a class="txt" href="convex4.html#E4:57_1_1_1"><i><font color="Green" title="E38">A1</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c7">w</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c5">v</font>
<b>by </b><i><a class="txt" href="convex4.html#E4:57_1_1_1"><i><font color="Green" title="E38">A1</font></i></a></i>
;<br/><b>thus </b><span class="p1">(<span class="default"><font color="Maroon" title="c6">u</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c5">v</font></span>)</span> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c7">w</font> = 
<font color="Maroon" title="c19">LK</font> <a href="convex4.html#K5" title="CONVEX4:func.5">+</a> <font color="Maroon" title="c18">M</font>
<b>by </b><i><a class="txt" href="convex4.html#E4:57_1_1_1"><i><font color="Green" title="E38">A1</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c17">L</font> <a href="convex4.html#K5" title="CONVEX4:func.5">+</a> <font color="Maroon" title="c16">K</font></span>)</span> <a href="convex4.html#K5" title="CONVEX4:func.5">+</a> <font color="Maroon" title="c18">M</font>
<b>by </b><i><a class="txt" href="convex4.html#E4:57_1_1_1"><i><font color="Green" title="E38">A1</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c17">L</font> <a href="convex4.html#K5" title="CONVEX4:func.5">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c16">K</font> <a href="convex4.html#K5" title="CONVEX4:func.5">+</a> <font color="Maroon" title="c18">M</font></span>)</span>
<b>by </b><i><a class="ref" href="convex4.html#T22" target="_self" title="CONVEX4:th.22">Th61</a></i>
<br/>.= 
<font color="Maroon" title="c17">L</font> <a href="convex4.html#K5" title="CONVEX4:func.5">+</a> <font color="Maroon" title="c20">KM</font>
<b>by </b><i><a class="txt" href="convex4.html#E4:57_1_1_1"><i><font color="Green" title="E38">A1</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c6">u</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c7">w</font></span>)</span>
<b>by </b><i><a class="txt" href="convex4.html#E4:57_1_1_1"><i><font color="Green" title="E38">A1</font></i></a></i>
;<br/><b>thus </b><font color="Maroon" title="c5">v</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="clvect_1.html#G1" title="CLVECT_1:aggr.1">CLSStruct</a>(# <span class="p1">(<span class="default"><a href="convex4.html#K10" title="CONVEX4:func.10">C_LinComb</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="convex4.html#K12" title="CONVEX4:func.12">@</a> <span class="p2">(<span class="default"><a href="convex4.html#K2" title="CONVEX4:func.2">ZeroCLC</a> <font color="Maroon" title="c1">V</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="convex4.html#K13" title="CONVEX4:func.13">C_LCAdd</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="convex4.html#K14" title="CONVEX4:func.14">C_LCMult</a> <font color="Maroon" title="c1">V</font></span>)</span> #)</span>)</span> = 
<font color="Maroon" title="c16">K</font> <a href="convex4.html#K5" title="CONVEX4:func.5">+</a> <span class="p1">(<span class="default"><a href="convex4.html#K2" title="CONVEX4:func.2">ZeroCLC</a> <font color="Maroon" title="c1">V</font></span>)</span>
<b>by </b><i><a class="txt" href="convex4.html#E4:57_1_1_1"><i><font color="Green" title="E38">A1</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c5">v</font>
<b>by </b><i><a class="ref" href="convex4.html#T23" target="_self" title="CONVEX4:th.23">Th62</a></i>
;<br/><a NAME="E9:57_1_1_1"/>
 <a href="convex4.html#K8" title="CONVEX4:func.8">-</a> <font color="Maroon" title="c16">K</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="clvect_1.html#G1" title="CLVECT_1:aggr.1">CLSStruct</a>(# <span class="p1">(<span class="default"><a href="convex4.html#K10" title="CONVEX4:func.10">C_LinComb</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="convex4.html#K12" title="CONVEX4:func.12">@</a> <span class="p2">(<span class="default"><a href="convex4.html#K2" title="CONVEX4:func.2">ZeroCLC</a> <font color="Maroon" title="c1">V</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="convex4.html#K13" title="CONVEX4:func.13">C_LCAdd</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="convex4.html#K14" title="CONVEX4:func.14">C_LCMult</a> <font color="Maroon" title="c1">V</font></span>)</span> #)
 <b>by </b><i><a class="ref" href="convex4.html#D12" target="_self" title="CONVEX4:def.12">Def8</a></i>;<br/><a NAME="E10:57_1_1_1"/><b>then </b>
 <a href="convex4.html#K8" title="CONVEX4:func.8">-</a> <font color="Maroon" title="c16">K</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a>  <a href="clvect_1.html#G1" title="CLVECT_1:aggr.1">CLSStruct</a>(# <span class="p1">(<span class="default"><a href="convex4.html#K10" title="CONVEX4:func.10">C_LinComb</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="convex4.html#K12" title="CONVEX4:func.12">@</a> <span class="p2">(<span class="default"><a href="convex4.html#K2" title="CONVEX4:func.2">ZeroCLC</a> <font color="Maroon" title="c1">V</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="convex4.html#K13" title="CONVEX4:func.13">C_LCAdd</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="convex4.html#K14" title="CONVEX4:func.14">C_LCMult</a> <font color="Maroon" title="c1">V</font></span>)</span> #)
 <b>by </b><i><a class="ref" href="struct_0.html#D5" title="STRUCT_0:def.5">STRUCT_0:def 5</a></i>;<br/><a NAME="E11:57_1_1_1"/><b>then </b>
 <a href="convex4.html#K8" title="CONVEX4:func.8">-</a> <font color="Maroon" title="c16">K</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rlvect_2.html#K1" title="RLVECT_2:func.1">vector</a> <a href="clvect_1.html#G1" title="CLVECT_1:aggr.1">CLSStruct</a>(# <span class="p1">(<span class="default"><a href="convex4.html#K10" title="CONVEX4:func.10">C_LinComb</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="convex4.html#K12" title="CONVEX4:func.12">@</a> <span class="p2">(<span class="default"><a href="convex4.html#K2" title="CONVEX4:func.2">ZeroCLC</a> <font color="Maroon" title="c1">V</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="convex4.html#K13" title="CONVEX4:func.13">C_LCAdd</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="convex4.html#K14" title="CONVEX4:func.14">C_LCMult</a> <font color="Maroon" title="c1">V</font></span>)</span> #),<span class="p1">(<span class="default"><a href="convex4.html#K8" title="CONVEX4:func.8">-</a> <font color="Maroon" title="c16">K</font></span>)</span>
 <b>by </b><i><a class="ref" href="rlvect_2.html#D1" title="RLVECT_2:def.1">RLVECT_2:def 1</a></i>;<br/><b>then </b><font color="Maroon" title="c5">v</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><a href="rlvect_2.html#K1" title="RLVECT_2:func.1">vector</a> <a href="clvect_1.html#G1" title="CLVECT_1:aggr.1">CLSStruct</a>(# <span class="p1">(<span class="default"><a href="convex4.html#K10" title="CONVEX4:func.10">C_LinComb</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="convex4.html#K12" title="CONVEX4:func.12">@</a> <span class="p2">(<span class="default"><a href="convex4.html#K2" title="CONVEX4:func.2">ZeroCLC</a> <font color="Maroon" title="c1">V</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="convex4.html#K13" title="CONVEX4:func.13">C_LCAdd</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="convex4.html#K14" title="CONVEX4:func.14">C_LCMult</a> <font color="Maroon" title="c1">V</font></span>)</span> #),<span class="p2">(<span class="default"><a href="convex4.html#K8" title="CONVEX4:func.8">-</a> <font color="Maroon" title="c16">K</font></span>)</span></span>)</span> = 
<font color="Maroon" title="c16">K</font> <a href="convex4.html#K9" title="CONVEX4:func.9">-</a> <font color="Maroon" title="c16">K</font>
<b>by </b><i><a class="txt" href="convex4.html#E4:57_1_1_1"><i><font color="Green" title="E38">A1</font></i></a></i>
<br/>.= 
 <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="clvect_1.html#G1" title="CLVECT_1:aggr.1">CLSStruct</a>(# <span class="p1">(<span class="default"><a href="convex4.html#K10" title="CONVEX4:func.10">C_LinComb</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="convex4.html#K12" title="CONVEX4:func.12">@</a> <span class="p2">(<span class="default"><a href="convex4.html#K2" title="CONVEX4:func.2">ZeroCLC</a> <font color="Maroon" title="c1">V</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="convex4.html#K13" title="CONVEX4:func.13">C_LCAdd</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="convex4.html#K14" title="CONVEX4:func.14">C_LCMult</a> <font color="Maroon" title="c1">V</font></span>)</span> #)
<b>by </b><i><a class="ref" href="convex4.html#T37" target="_self" title="CONVEX4:th.37">Th82</a></i>
;<br/><b>hence </b><a NAME="E13:57_1_1_1"/>
 ex <font color="Olive" title="b1">w</font> being  <a href="clvect_1.html#NM1" title="CLVECT_1:NM.1">VECTOR</a> of <a href="clvect_1.html#G1" title="CLVECT_1:aggr.1">CLSStruct</a>(# <span class="p1">(<span class="default"><a href="convex4.html#K10" title="CONVEX4:func.10">C_LinComb</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="convex4.html#K12" title="CONVEX4:func.12">@</a> <span class="p2">(<span class="default"><a href="convex4.html#K2" title="CONVEX4:func.2">ZeroCLC</a> <font color="Maroon" title="c1">V</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="convex4.html#K13" title="CONVEX4:func.13">C_LCAdd</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="convex4.html#K14" title="CONVEX4:func.14">C_LCMult</a> <font color="Maroon" title="c1">V</font></span>)</span> #) st <font color="Maroon" title="c5">v</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Olive" title="b1">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="clvect_1.html#G1" title="CLVECT_1:aggr.1">CLSStruct</a>(# <span class="p1">(<span class="default"><a href="convex4.html#K10" title="CONVEX4:func.10">C_LinComb</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="convex4.html#K12" title="CONVEX4:func.12">@</a> <span class="p2">(<span class="default"><a href="convex4.html#K2" title="CONVEX4:func.2">ZeroCLC</a> <font color="Maroon" title="c1">V</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="convex4.html#K13" title="CONVEX4:func.13">C_LCAdd</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="convex4.html#K14" title="CONVEX4:func.14">C_LCMult</a> <font color="Maroon" title="c1">V</font></span>)</span> #)
 ;<br/><b>thus </b><font color="Maroon" title="c3">a</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c7">w</font></span>)</span> = 
<font color="Maroon" title="c3">a</font> <a href="convex4.html#K7" title="CONVEX4:func.7">*</a> <font color="Maroon" title="c20">KM</font>
<b>by </b><i><a class="txt" href="convex4.html#E5:57_1_1_1"><i><font color="Green" title="E39">A4</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c3">a</font> <a href="convex4.html#K7" title="CONVEX4:func.7">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c16">K</font> <a href="convex4.html#K5" title="CONVEX4:func.5">+</a> <font color="Maroon" title="c18">M</font></span>)</span>
<b>by </b><i><a class="txt" href="convex4.html#E4:57_1_1_1"><i><font color="Green" title="E38">A1</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="convex4.html#K7" title="CONVEX4:func.7">*</a> <font color="Maroon" title="c16">K</font></span>)</span> <a href="convex4.html#K5" title="CONVEX4:func.5">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="convex4.html#K7" title="CONVEX4:func.7">*</a> <font color="Maroon" title="c18">M</font></span>)</span>
<b>by </b><i><a class="ref" href="convex4.html#T28" target="_self" title="CONVEX4:th.28">Th69</a></i>
<br/>.= 
<font color="Maroon" title="c21">aK</font> <a href="convex4.html#K5" title="CONVEX4:func.5">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="convex4.html#K7" title="CONVEX4:func.7">*</a> <font color="Maroon" title="c18">M</font></span>)</span>
<b>by </b><i><a class="txt" href="convex4.html#E5:57_1_1_1"><i><font color="Green" title="E39">A4</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c21">aK</font> <a href="convex4.html#K5" title="CONVEX4:func.5">+</a> <font color="Maroon" title="c22">aM</font>
<b>by </b><i><a class="txt" href="convex4.html#E5:57_1_1_1"><i><font color="Green" title="E39">A4</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c5">v</font></span>)</span> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c7">w</font></span>)</span>
<b>by </b><i><a class="txt" href="convex4.html#E4:57_1_1_1"><i><font color="Green" title="E38">A1</font></i></a></i>
;<br/><b>thus </b><span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="complex1.html#K8" title="COMPLEX1:func.8">+</a> <font color="Maroon" title="c4">b</font></span>)</span> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c5">v</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="complex1.html#K8" title="COMPLEX1:func.8">+</a> <font color="Maroon" title="c4">b</font></span>)</span> <a href="convex4.html#K7" title="CONVEX4:func.7">*</a> <font color="Maroon" title="c16">K</font>
<b>by </b><i><a class="txt" href="convex4.html#E5:57_1_1_1"><i><font color="Green" title="E39">A4</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="convex4.html#K7" title="CONVEX4:func.7">*</a> <font color="Maroon" title="c16">K</font></span>)</span> <a href="convex4.html#K5" title="CONVEX4:func.5">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="convex4.html#K7" title="CONVEX4:func.7">*</a> <font color="Maroon" title="c16">K</font></span>)</span>
<b>by </b><i><a class="ref" href="convex4.html#T27" target="_self" title="CONVEX4:th.27">Th68</a></i>
<br/>.= 
<font color="Maroon" title="c21">aK</font> <a href="convex4.html#K5" title="CONVEX4:func.5">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="convex4.html#K7" title="CONVEX4:func.7">*</a> <font color="Maroon" title="c16">K</font></span>)</span>
<b>by </b><i><a class="txt" href="convex4.html#E5:57_1_1_1"><i><font color="Green" title="E39">A4</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c21">aK</font> <a href="convex4.html#K5" title="CONVEX4:func.5">+</a> <font color="Maroon" title="c23">bK</font>
<b>by </b><i><a class="txt" href="convex4.html#E5:57_1_1_1"><i><font color="Green" title="E39">A4</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c5">v</font></span>)</span> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c5">v</font></span>)</span>
<b>by </b><i><a class="txt" href="convex4.html#E4:57_1_1_1"><i><font color="Green" title="E38">A1</font></i></a></i>
;<br/><b>thus </b><span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <font color="Maroon" title="c4">b</font></span>)</span> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c5">v</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <font color="Maroon" title="c4">b</font></span>)</span> <a href="convex4.html#K7" title="CONVEX4:func.7">*</a> <font color="Maroon" title="c16">K</font>
<b>by </b><i><a class="txt" href="convex4.html#E5:57_1_1_1"><i><font color="Green" title="E39">A4</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c3">a</font> <a href="convex4.html#K7" title="CONVEX4:func.7">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="convex4.html#K7" title="CONVEX4:func.7">*</a> <font color="Maroon" title="c16">K</font></span>)</span>
<b>by </b><i><a class="ref" href="convex4.html#T29" target="_self" title="CONVEX4:th.29">Th70</a></i>
<br/>.= 
<font color="Maroon" title="c3">a</font> <a href="convex4.html#K7" title="CONVEX4:func.7">*</a> <font color="Maroon" title="c23">bK</font>
<b>by </b><i><a class="txt" href="convex4.html#E5:57_1_1_1"><i><font color="Green" title="E39">A4</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c3">a</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c5">v</font></span>)</span>
<b>by </b><i><a class="txt" href="convex4.html#E5:57_1_1_1"><i><font color="Green" title="E39">A4</font></i></a></i>
;<br/><b>thus </b><a href="complex1.html#K6" title="COMPLEX1:func.6">1r</a>  <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c5">v</font> = 
<a href="complex1.html#K6" title="COMPLEX1:func.6">1r</a>  <a href="convex4.html#K7" title="CONVEX4:func.7">*</a> <font color="Maroon" title="c16">K</font>
<b>by </b><i><a class="txt" href="convex4.html#E5:57_1_1_1"><i><font color="Green" title="E39">A4</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c5">v</font>
<b>by </b><i><a class="ref" href="convex4.html#T30" target="_self" title="CONVEX4:th.30">Th71</a></i>
;<br/></div><b>end;</b></div>
<a NAME="E2:57_1_1"/><b>then </b><i><font color="Green" title="E38">X1</font></i>: 
( ( for <font color="Olive" title="b1">v</font>, <font color="Olive" title="b2">w</font> being  <a href="clvect_1.html#NM1" title="CLVECT_1:NM.1">VECTOR</a> of <a href="clvect_1.html#G1" title="CLVECT_1:aggr.1">CLSStruct</a>(# <span class="p1">(<span class="default"><a href="convex4.html#K10" title="CONVEX4:func.10">C_LinComb</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="convex4.html#K12" title="CONVEX4:func.12">@</a> <span class="p2">(<span class="default"><a href="convex4.html#K2" title="CONVEX4:func.2">ZeroCLC</a> <font color="Maroon" title="c1">V</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="convex4.html#K13" title="CONVEX4:func.13">C_LCAdd</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="convex4.html#K14" title="CONVEX4:func.14">C_LCMult</a> <font color="Maroon" title="c1">V</font></span>)</span> #) holds  <font color="Olive" title="b1">v</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Olive" title="b2">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">w</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Olive" title="b1">v</font> ) &amp; ( for <font color="Olive" title="b1">u</font>, <font color="Olive" title="b2">v</font>, <font color="Olive" title="b3">w</font> being  <a href="clvect_1.html#NM1" title="CLVECT_1:NM.1">VECTOR</a> of <a href="clvect_1.html#G1" title="CLVECT_1:aggr.1">CLSStruct</a>(# <span class="p1">(<span class="default"><a href="convex4.html#K10" title="CONVEX4:func.10">C_LinComb</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="convex4.html#K12" title="CONVEX4:func.12">@</a> <span class="p2">(<span class="default"><a href="convex4.html#K2" title="CONVEX4:func.2">ZeroCLC</a> <font color="Maroon" title="c1">V</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="convex4.html#K13" title="CONVEX4:func.13">C_LCAdd</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="convex4.html#K14" title="CONVEX4:func.14">C_LCMult</a> <font color="Maroon" title="c1">V</font></span>)</span> #) holds  <span class="p1">(<span class="default"><font color="Olive" title="b1">u</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Olive" title="b2">v</font></span>)</span> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Olive" title="b3">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">u</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">v</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Olive" title="b3">w</font></span>)</span> ) &amp; ( for <font color="Olive" title="b1">v</font> being  <a href="clvect_1.html#NM1" title="CLVECT_1:NM.1">VECTOR</a> of <a href="clvect_1.html#G1" title="CLVECT_1:aggr.1">CLSStruct</a>(# <span class="p1">(<span class="default"><a href="convex4.html#K10" title="CONVEX4:func.10">C_LinComb</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="convex4.html#K12" title="CONVEX4:func.12">@</a> <span class="p2">(<span class="default"><a href="convex4.html#K2" title="CONVEX4:func.2">ZeroCLC</a> <font color="Maroon" title="c1">V</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="convex4.html#K13" title="CONVEX4:func.13">C_LCAdd</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="convex4.html#K14" title="CONVEX4:func.14">C_LCMult</a> <font color="Maroon" title="c1">V</font></span>)</span> #) holds  <font color="Olive" title="b1">v</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="clvect_1.html#G1" title="CLVECT_1:aggr.1">CLSStruct</a>(# <span class="p1">(<span class="default"><a href="convex4.html#K10" title="CONVEX4:func.10">C_LinComb</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="convex4.html#K12" title="CONVEX4:func.12">@</a> <span class="p2">(<span class="default"><a href="convex4.html#K2" title="CONVEX4:func.2">ZeroCLC</a> <font color="Maroon" title="c1">V</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="convex4.html#K13" title="CONVEX4:func.13">C_LCAdd</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="convex4.html#K14" title="CONVEX4:func.14">C_LCMult</a> <font color="Maroon" title="c1">V</font></span>)</span> #)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">v</font> ) &amp; ( for <font color="Olive" title="b1">v</font> being  <a href="clvect_1.html#NM1" title="CLVECT_1:NM.1">VECTOR</a> of <a href="clvect_1.html#G1" title="CLVECT_1:aggr.1">CLSStruct</a>(# <span class="p1">(<span class="default"><a href="convex4.html#K10" title="CONVEX4:func.10">C_LinComb</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="convex4.html#K12" title="CONVEX4:func.12">@</a> <span class="p2">(<span class="default"><a href="convex4.html#K2" title="CONVEX4:func.2">ZeroCLC</a> <font color="Maroon" title="c1">V</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="convex4.html#K13" title="CONVEX4:func.13">C_LCAdd</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="convex4.html#K14" title="CONVEX4:func.14">C_LCMult</a> <font color="Maroon" title="c1">V</font></span>)</span> #)  ex <font color="Olive" title="b2">w</font> being  <a href="clvect_1.html#NM1" title="CLVECT_1:NM.1">VECTOR</a> of <a href="clvect_1.html#G1" title="CLVECT_1:aggr.1">CLSStruct</a>(# <span class="p1">(<span class="default"><a href="convex4.html#K10" title="CONVEX4:func.10">C_LinComb</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="convex4.html#K12" title="CONVEX4:func.12">@</a> <span class="p2">(<span class="default"><a href="convex4.html#K2" title="CONVEX4:func.2">ZeroCLC</a> <font color="Maroon" title="c1">V</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="convex4.html#K13" title="CONVEX4:func.13">C_LCAdd</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="convex4.html#K14" title="CONVEX4:func.14">C_LCMult</a> <font color="Maroon" title="c1">V</font></span>)</span> #) st <font color="Olive" title="b1">v</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Olive" title="b2">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="clvect_1.html#G1" title="CLVECT_1:aggr.1">CLSStruct</a>(# <span class="p1">(<span class="default"><a href="convex4.html#K10" title="CONVEX4:func.10">C_LinComb</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="convex4.html#K12" title="CONVEX4:func.12">@</a> <span class="p2">(<span class="default"><a href="convex4.html#K2" title="CONVEX4:func.2">ZeroCLC</a> <font color="Maroon" title="c1">V</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="convex4.html#K13" title="CONVEX4:func.13">C_LCAdd</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="convex4.html#K14" title="CONVEX4:func.14">C_LCMult</a> <font color="Maroon" title="c1">V</font></span>)</span> #) ) &amp; ( for <font color="Olive" title="b1">a</font> being  <a href="cfunct_1.html#NM1" title="CFUNCT_1:NM.1">Complex</a><br/> for <font color="Olive" title="b2">v</font>, <font color="Olive" title="b3">w</font> being  <a href="clvect_1.html#NM1" title="CLVECT_1:NM.1">VECTOR</a> of <a href="clvect_1.html#G1" title="CLVECT_1:aggr.1">CLSStruct</a>(# <span class="p1">(<span class="default"><a href="convex4.html#K10" title="CONVEX4:func.10">C_LinComb</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="convex4.html#K12" title="CONVEX4:func.12">@</a> <span class="p2">(<span class="default"><a href="convex4.html#K2" title="CONVEX4:func.2">ZeroCLC</a> <font color="Maroon" title="c1">V</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="convex4.html#K13" title="CONVEX4:func.13">C_LCAdd</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="convex4.html#K14" title="CONVEX4:func.14">C_LCMult</a> <font color="Maroon" title="c1">V</font></span>)</span> #) holds  <font color="Olive" title="b1">a</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">v</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Olive" title="b3">w</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">a</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Olive" title="b2">v</font></span>)</span> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">a</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Olive" title="b3">w</font></span>)</span> ) &amp; ( for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being  <a href="cfunct_1.html#NM1" title="CFUNCT_1:NM.1">Complex</a><br/> for <font color="Olive" title="b3">v</font> being  <a href="clvect_1.html#NM1" title="CLVECT_1:NM.1">VECTOR</a> of <a href="clvect_1.html#G1" title="CLVECT_1:aggr.1">CLSStruct</a>(# <span class="p1">(<span class="default"><a href="convex4.html#K10" title="CONVEX4:func.10">C_LinComb</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="convex4.html#K12" title="CONVEX4:func.12">@</a> <span class="p2">(<span class="default"><a href="convex4.html#K2" title="CONVEX4:func.2">ZeroCLC</a> <font color="Maroon" title="c1">V</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="convex4.html#K13" title="CONVEX4:func.13">C_LCAdd</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="convex4.html#K14" title="CONVEX4:func.14">C_LCMult</a> <font color="Maroon" title="c1">V</font></span>)</span> #) holds  <span class="p1">(<span class="default"><font color="Olive" title="b1">a</font> <a href="complex1.html#K8" title="COMPLEX1:func.8">+</a> <font color="Olive" title="b2">b</font></span>)</span> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Olive" title="b3">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">a</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Olive" title="b3">v</font></span>)</span> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">b</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Olive" title="b3">v</font></span>)</span> ) &amp; ( for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being  <a href="cfunct_1.html#NM1" title="CFUNCT_1:NM.1">Complex</a><br/> for <font color="Olive" title="b3">v</font> being  <a href="clvect_1.html#NM1" title="CLVECT_1:NM.1">VECTOR</a> of <a href="clvect_1.html#G1" title="CLVECT_1:aggr.1">CLSStruct</a>(# <span class="p1">(<span class="default"><a href="convex4.html#K10" title="CONVEX4:func.10">C_LinComb</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="convex4.html#K12" title="CONVEX4:func.12">@</a> <span class="p2">(<span class="default"><a href="convex4.html#K2" title="CONVEX4:func.2">ZeroCLC</a> <font color="Maroon" title="c1">V</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="convex4.html#K13" title="CONVEX4:func.13">C_LCAdd</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="convex4.html#K14" title="CONVEX4:func.14">C_LCMult</a> <font color="Maroon" title="c1">V</font></span>)</span> #) holds  <span class="p1">(<span class="default"><font color="Olive" title="b1">a</font> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <font color="Olive" title="b2">b</font></span>)</span> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Olive" title="b3">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">b</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Olive" title="b3">v</font></span>)</span> ) &amp; ( for <font color="Olive" title="b1">v</font> being  <a href="clvect_1.html#NM1" title="CLVECT_1:NM.1">VECTOR</a> of <a href="clvect_1.html#G1" title="CLVECT_1:aggr.1">CLSStruct</a>(# <span class="p1">(<span class="default"><a href="convex4.html#K10" title="CONVEX4:func.10">C_LinComb</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="convex4.html#K12" title="CONVEX4:func.12">@</a> <span class="p2">(<span class="default"><a href="convex4.html#K2" title="CONVEX4:func.2">ZeroCLC</a> <font color="Maroon" title="c1">V</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="convex4.html#K13" title="CONVEX4:func.13">C_LCAdd</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="convex4.html#K14" title="CONVEX4:func.14">C_LCMult</a> <font color="Maroon" title="c1">V</font></span>)</span> #) holds  <a href="complex1.html#K6" title="COMPLEX1:func.6">1r</a>  <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Olive" title="b1">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">v</font> ) )
 
;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="57_1_1_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c3">v</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="clvect_1.html#G1" title="CLVECT_1:aggr.1">CLSStruct</a>(# <span class="p1">(<span class="default"><a href="convex4.html#K10" title="CONVEX4:func.10">C_LinComb</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="convex4.html#K12" title="CONVEX4:func.12">@</a> <span class="p2">(<span class="default"><a href="convex4.html#K2" title="CONVEX4:func.2">ZeroCLC</a> <font color="Maroon" title="c1">V</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="convex4.html#K13" title="CONVEX4:func.13">C_LCAdd</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="convex4.html#K14" title="CONVEX4:func.14">C_LCMult</a> <font color="Maroon" title="c1">V</font></span>)</span> #);<br/><a NAME="E1:57_1_1_2"/>
 ex <font color="Olive" title="b1">w</font> being  <a href="clvect_1.html#NM1" title="CLVECT_1:NM.1">VECTOR</a> of <a href="clvect_1.html#G1" title="CLVECT_1:aggr.1">CLSStruct</a>(# <span class="p1">(<span class="default"><a href="convex4.html#K10" title="CONVEX4:func.10">C_LinComb</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="convex4.html#K12" title="CONVEX4:func.12">@</a> <span class="p2">(<span class="default"><a href="convex4.html#K2" title="CONVEX4:func.2">ZeroCLC</a> <font color="Maroon" title="c1">V</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="convex4.html#K13" title="CONVEX4:func.13">C_LCAdd</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="convex4.html#K14" title="CONVEX4:func.14">C_LCMult</a> <font color="Maroon" title="c1">V</font></span>)</span> #) st <font color="Maroon" title="c3">v</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Olive" title="b1">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="clvect_1.html#G1" title="CLVECT_1:aggr.1">CLSStruct</a>(# <span class="p1">(<span class="default"><a href="convex4.html#K10" title="CONVEX4:func.10">C_LinComb</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="convex4.html#K12" title="CONVEX4:func.12">@</a> <span class="p2">(<span class="default"><a href="convex4.html#K2" title="CONVEX4:func.2">ZeroCLC</a> <font color="Maroon" title="c1">V</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="convex4.html#K13" title="CONVEX4:func.13">C_LCAdd</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="convex4.html#K14" title="CONVEX4:func.14">C_LCMult</a> <font color="Maroon" title="c1">V</font></span>)</span> #)
 <b>by </b><i><a class="txt" href="convex4.html#E1:57_1_1"><i><font color="Green" title="E37">X0</font></i></a></i>;<br/><b>hence </b><a NAME="E2:57_1_1_2"/>
<font color="Maroon" title="c3">v</font> is <a href="algstr_0.html#V10" title="ALGSTR_0:attr.10">right_complementable</a>
 <b>by </b><i><a class="ref" href="algstr_0.html#D11" title="ALGSTR_0:def.11">ALGSTR_0:def 11</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:57_1_1"/>
 <a href="clvect_1.html#G1" title="CLVECT_1:aggr.1">CLSStruct</a>(# <span class="p1">(<span class="default"><a href="convex4.html#K10" title="CONVEX4:func.10">C_LinComb</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="convex4.html#K12" title="CONVEX4:func.12">@</a> <span class="p2">(<span class="default"><a href="convex4.html#K2" title="CONVEX4:func.2">ZeroCLC</a> <font color="Maroon" title="c1">V</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="convex4.html#K13" title="CONVEX4:func.13">C_LCAdd</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="convex4.html#K14" title="CONVEX4:func.14">C_LCMult</a> <font color="Maroon" title="c1">V</font></span>)</span> #) is   <a href="clvect_1.html#NM2" title="CLVECT_1:NM.2">ComplexLinearSpace</a>
 <b>by </b><i><a class="txt" href="convex4.html#E2:57_1_1"><i><font color="Green" title="E38">X1</font></i></a>, <a class="ref" href="clvect_1.html#D2" title="CLVECT_1:def.2">CLVECT_1:def 2</a>, <a class="ref" href="rlvect_1.html#D5" title="RLVECT_1:def.5">RLVECT_1:def 5</a>, <a class="ref" href="rlvect_1.html#D6" title="RLVECT_1:def.6">RLVECT_1:def 6</a>, <a class="ref" href="rlvect_1.html#D7" title="RLVECT_1:def.7">RLVECT_1:def 7</a>, <a class="ref" href="algstr_0.html#D16" title="ALGSTR_0:def.16">ALGSTR_0:def 16</a></i>;<br/>


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