<?xml version="1.0"?>
<div class="add">

<b>set </b><font color="Maroon" title="c2">S</font> =  <a href="rlvect_1.html#G2" title="RLVECT_1:aggr.2">RLSStruct</a>(# <span class="p1">(<span class="default"><a href="rlvect_2.html#K11" title="RLVECT_2:func.11">LinComb</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="rlvect_2.html#K13" title="RLVECT_2:func.13">@</a> <span class="p2">(<span class="default"><a href="rlvect_2.html#K4" title="RLVECT_2:func.4">ZeroLC</a> <font color="Maroon" title="c1">V</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="rlvect_2.html#K14" title="RLVECT_2:func.14">LCAdd</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="rlvect_2.html#K15" title="RLVECT_2:func.15">LCMult</a> <font color="Maroon" title="c1">V</font></span>)</span> #);<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="77_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="real_1.html#NM1" title="REAL_1:NM.1">Real</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="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <a href="rlvect_1.html#G2" title="RLVECT_1:aggr.2">RLSStruct</a>(# <span class="p1">(<span class="default"><a href="rlvect_2.html#K11" title="RLVECT_2:func.11">LinComb</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="rlvect_2.html#K13" title="RLVECT_2:func.13">@</a> <span class="p2">(<span class="default"><a href="rlvect_2.html#K4" title="RLVECT_2:func.4">ZeroLC</a> <font color="Maroon" title="c1">V</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="rlvect_2.html#K14" title="RLVECT_2:func.14">LCAdd</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="rlvect_2.html#K15" title="RLVECT_2:func.15">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="rlvect_1.html#K1" title="RLVECT_1: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="rlvect_1.html#K1" title="RLVECT_1: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="rlvect_1.html#K2" title="RLVECT_1:func.2">*</a> <font color="Maroon" title="c5">v</font>, <font color="Maroon" title="c14">az</font> = <font color="Maroon" title="c3">a</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">*</a> <font color="Maroon" title="c7">w</font>, <font color="Maroon" title="c15">bx</font> = <font color="Maroon" title="c4">b</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">*</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="rlvect_2.html#K11" title="RLVECT_2:func.11">LinComb</a> <font color="Maroon" title="c1">V</font> ;<br/><a NAME="E2:77_1_1_1"/>
(  <a href="rlvect_2.html#K12" title="RLVECT_2:func.12">@</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="rlvect_2.html#K12" title="RLVECT_2:func.12">@</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="rlvect_2.html#K12" title="RLVECT_2:func.12">@</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="rlvect_2.html#K12" title="RLVECT_2:func.12">@</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="rlvect_1.html#K1" title="RLVECT_1:func.1">+</a> <font color="Maroon" title="c5">v</font> &amp;  <a href="rlvect_2.html#K12" title="RLVECT_2:func.12">@</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="rlvect_1.html#K1" title="RLVECT_1:func.1">+</a> <font color="Maroon" title="c7">w</font> &amp;  <a href="rlvect_2.html#K12" title="RLVECT_2:func.12">@</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="rlvect_1.html#K2" title="RLVECT_1:func.2">*</a> <font color="Maroon" title="c5">v</font> &amp;  <a href="rlvect_2.html#K12" title="RLVECT_2:func.12">@</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="rlvect_1.html#K2" title="RLVECT_1:func.2">*</a> <font color="Maroon" title="c7">w</font> &amp;  <a href="rlvect_2.html#K12" title="RLVECT_2:func.12">@</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="rlvect_1.html#K2" title="RLVECT_1:func.2">*</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="rlvect_1.html#K1" title="RLVECT_1: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="rlvect_1.html#K1" title="RLVECT_1: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="rlvect_1.html#K2" title="RLVECT_1:func.2">*</a> <font color="Maroon" title="c5">v</font>, <font color="Maroon" title="c22">aM</font> = <font color="Maroon" title="c3">a</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">*</a> <font color="Maroon" title="c7">w</font>, <font color="Maroon" title="c23">bK</font> = <font color="Maroon" title="c4">b</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">*</a> <font color="Maroon" title="c5">v</font> as    <a href="rlvect_2.html#M1" title="RLVECT_2:mode.1">Linear_Combination</a> of <font color="Maroon" title="c1">V</font> ;<br/><div><i><font color="Green" title="E46">A1</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="77_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="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <a href="rlvect_1.html#G2" title="RLVECT_1:aggr.2">RLSStruct</a>(# <span class="p1">(<span class="default"><a href="rlvect_2.html#K11" title="RLVECT_2:func.11">LinComb</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="rlvect_2.html#K13" title="RLVECT_2:func.13">@</a> <span class="p2">(<span class="default"><a href="rlvect_2.html#K4" title="RLVECT_2:func.4">ZeroLC</a> <font color="Maroon" title="c1">V</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="rlvect_2.html#K14" title="RLVECT_2:func.14">LCAdd</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="rlvect_2.html#K15" title="RLVECT_2:func.15">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="rlvect_2.html#M1" title="RLVECT_2:mode.1">Linear_Combination</a> of <font color="Maroon" title="c1">V</font>;<br/><b>assume </b><a NAME="E1:77_1_1_1_1"/><i><font color="Green" title="E47">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="E2:77_1_1_1_1"/>
(  <a href="rlvect_2.html#K12" title="RLVECT_2:func.12">@</a> <span class="p1">(<span class="default"><a href="rlvect_2.html#K13" title="RLVECT_2:func.13">@</a> <font color="Maroon" title="c26">K</font></span>)</span> <a href="rlvect_2.html#R1" title="RLVECT_2:pred.1">=</a> <font color="Maroon" title="c26">K</font> &amp;  <a href="rlvect_2.html#K12" title="RLVECT_2:func.12">@</a> <span class="p1">(<span class="default"><a href="rlvect_2.html#K13" title="RLVECT_2:func.13">@</a> <font color="Maroon" title="c27">L</font></span>)</span> <a href="rlvect_2.html#R1" title="RLVECT_2:pred.1">=</a> <font color="Maroon" title="c27">L</font> )
 ;<br/><b>hence </b><a NAME="E3:77_1_1_1_1"/>
<font color="Maroon" title="c24">v</font> <a href="rlvect_1.html#K1" title="RLVECT_1: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="rlvect_2.html#K7" title="RLVECT_2:func.7">+</a> <font color="Maroon" title="c27">L</font>
 <b>by </b><i><a class="txt" href="rlvect_2.html#E1:77_1_1_1_1"><i><font color="Green" title="E47">A2</font></i></a>, <a class="ref" href="rlvect_2.html#D19" target="_self" title="RLVECT_2:def.19">Def19</a></i>;<br/></div><b>end;</b></div><div><i><font color="Green" title="E47">A3</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="77_1_1_1_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c24">v</font> be   <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <a href="rlvect_1.html#G2" title="RLVECT_1:aggr.2">RLSStruct</a>(# <span class="p1">(<span class="default"><a href="rlvect_2.html#K11" title="RLVECT_2:func.11">LinComb</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="rlvect_2.html#K13" title="RLVECT_2:func.13">@</a> <span class="p2">(<span class="default"><a href="rlvect_2.html#K4" title="RLVECT_2:func.4">ZeroLC</a> <font color="Maroon" title="c1">V</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="rlvect_2.html#K14" title="RLVECT_2:func.14">LCAdd</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="rlvect_2.html#K15" title="RLVECT_2:func.15">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="rlvect_2.html#M1" title="RLVECT_2:mode.1">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="real_1.html#NM1" title="REAL_1:NM.1">Real</a>;<br/><b>assume </b><a NAME="E1:77_1_1_1_2"/><i><font color="Green" title="E48">A4</font></i>: 
<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="E2:77_1_1_1_2"/>
 <a href="rlvect_2.html#K12" title="RLVECT_2:func.12">@</a> <span class="p1">(<span class="default"><a href="rlvect_2.html#K13" title="RLVECT_2:func.13">@</a> <font color="Maroon" title="c25">L</font></span>)</span> <a href="rlvect_2.html#R1" title="RLVECT_2:pred.1">=</a> <font color="Maroon" title="c25">L</font>
 ;<br/><b>hence </b><a NAME="E3:77_1_1_1_2"/>
<font color="Maroon" title="c26">a</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">*</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="rlvect_2.html#K8" title="RLVECT_2:func.8">*</a> <font color="Maroon" title="c25">L</font>
 <b>by </b><i><a class="txt" href="rlvect_2.html#E1:77_1_1_1_2"><i><font color="Green" title="E48">A4</font></i></a>, <a class="ref" href="rlvect_2.html#D20" target="_self" title="RLVECT_2:def.20">Def20</a></i>;<br/></div><b>end;</b></div><b>thus </b><font color="Maroon" title="c5">v</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">+</a> <font color="Maroon" title="c7">w</font> = 
<font color="Maroon" title="c16">K</font> <a href="rlvect_2.html#K7" title="RLVECT_2:func.7">+</a> <font color="Maroon" title="c18">M</font>
<b>by </b><i><a class="txt" href="rlvect_2.html#E4:77_1_1_1"><i><font color="Green" title="E46">A1</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c18">M</font> <a href="rlvect_2.html#K7" title="RLVECT_2:func.7">+</a> <font color="Maroon" title="c16">K</font>
<b>by </b><i><a class="ref" href="rlvect_2.html#T60" target="_self" title="RLVECT_2:th.60">Th60</a></i>
<br/>.= 
<font color="Maroon" title="c7">w</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">+</a> <font color="Maroon" title="c5">v</font>
<b>by </b><i><a class="txt" href="rlvect_2.html#E4:77_1_1_1"><i><font color="Green" title="E46">A1</font></i></a></i>
;<br/><b>thus </b><span class="p1">(<span class="default"><font color="Maroon" title="c6">u</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">+</a> <font color="Maroon" title="c5">v</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">+</a> <font color="Maroon" title="c7">w</font> = 
<font color="Maroon" title="c19">LK</font> <a href="rlvect_2.html#K7" title="RLVECT_2:func.7">+</a> <font color="Maroon" title="c18">M</font>
<b>by </b><i><a class="txt" href="rlvect_2.html#E4:77_1_1_1"><i><font color="Green" title="E46">A1</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c17">L</font> <a href="rlvect_2.html#K7" title="RLVECT_2:func.7">+</a> <font color="Maroon" title="c16">K</font></span>)</span> <a href="rlvect_2.html#K7" title="RLVECT_2:func.7">+</a> <font color="Maroon" title="c18">M</font>
<b>by </b><i><a class="txt" href="rlvect_2.html#E4:77_1_1_1"><i><font color="Green" title="E46">A1</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c17">L</font> <a href="rlvect_2.html#K7" title="RLVECT_2:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c16">K</font> <a href="rlvect_2.html#K7" title="RLVECT_2:func.7">+</a> <font color="Maroon" title="c18">M</font></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_2.html#T61" target="_self" title="RLVECT_2:th.61">Th61</a></i>
<br/>.= 
<font color="Maroon" title="c17">L</font> <a href="rlvect_2.html#K7" title="RLVECT_2:func.7">+</a> <font color="Maroon" title="c20">KM</font>
<b>by </b><i><a class="txt" href="rlvect_2.html#E4:77_1_1_1"><i><font color="Green" title="E46">A1</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c6">u</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">+</a> <font color="Maroon" title="c7">w</font></span>)</span>
<b>by </b><i><a class="txt" href="rlvect_2.html#E4:77_1_1_1"><i><font color="Green" title="E46">A1</font></i></a></i>
;<br/><b>thus </b><font color="Maroon" title="c5">v</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">+</a> <span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="rlvect_1.html#G2" title="RLVECT_1:aggr.2">RLSStruct</a>(# <span class="p1">(<span class="default"><a href="rlvect_2.html#K11" title="RLVECT_2:func.11">LinComb</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="rlvect_2.html#K13" title="RLVECT_2:func.13">@</a> <span class="p2">(<span class="default"><a href="rlvect_2.html#K4" title="RLVECT_2:func.4">ZeroLC</a> <font color="Maroon" title="c1">V</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="rlvect_2.html#K14" title="RLVECT_2:func.14">LCAdd</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="rlvect_2.html#K15" title="RLVECT_2:func.15">LCMult</a> <font color="Maroon" title="c1">V</font></span>)</span> #)</span>)</span> = 
<font color="Maroon" title="c16">K</font> <a href="rlvect_2.html#K7" title="RLVECT_2:func.7">+</a> <span class="p1">(<span class="default"><a href="rlvect_2.html#K4" title="RLVECT_2:func.4">ZeroLC</a> <font color="Maroon" title="c1">V</font></span>)</span>
<b>by </b><i><a class="txt" href="rlvect_2.html#E4:77_1_1_1"><i><font color="Green" title="E46">A1</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c5">v</font>
<b>by </b><i><a class="ref" href="rlvect_2.html#T62" target="_self" title="RLVECT_2:th.62">Th62</a></i>
;<br/><a NAME="E9:77_1_1_1"/>
 <a href="rlvect_2.html#K9" title="RLVECT_2:func.9">-</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="rlvect_1.html#G2" title="RLVECT_1:aggr.2">RLSStruct</a>(# <span class="p1">(<span class="default"><a href="rlvect_2.html#K11" title="RLVECT_2:func.11">LinComb</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="rlvect_2.html#K13" title="RLVECT_2:func.13">@</a> <span class="p2">(<span class="default"><a href="rlvect_2.html#K4" title="RLVECT_2:func.4">ZeroLC</a> <font color="Maroon" title="c1">V</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="rlvect_2.html#K14" title="RLVECT_2:func.14">LCAdd</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="rlvect_2.html#K15" title="RLVECT_2:func.15">LCMult</a> <font color="Maroon" title="c1">V</font></span>)</span> #)
 <b>by </b><i><a class="ref" href="rlvect_2.html#D16" target="_self" title="RLVECT_2:def.16">Def16</a></i>;<br/><a NAME="E10:77_1_1_1"/><b>then </b>
 <a href="rlvect_2.html#K9" title="RLVECT_2:func.9">-</a> <font color="Maroon" title="c16">K</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a>  <a href="rlvect_1.html#G2" title="RLVECT_1:aggr.2">RLSStruct</a>(# <span class="p1">(<span class="default"><a href="rlvect_2.html#K11" title="RLVECT_2:func.11">LinComb</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="rlvect_2.html#K13" title="RLVECT_2:func.13">@</a> <span class="p2">(<span class="default"><a href="rlvect_2.html#K4" title="RLVECT_2:func.4">ZeroLC</a> <font color="Maroon" title="c1">V</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="rlvect_2.html#K14" title="RLVECT_2:func.14">LCAdd</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="rlvect_2.html#K15" title="RLVECT_2:func.15">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="E11:77_1_1_1"/><b>then </b>
 <a href="rlvect_2.html#K9" title="RLVECT_2:func.9">-</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="rlvect_1.html#G2" title="RLVECT_1:aggr.2">RLSStruct</a>(# <span class="p1">(<span class="default"><a href="rlvect_2.html#K11" title="RLVECT_2:func.11">LinComb</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="rlvect_2.html#K13" title="RLVECT_2:func.13">@</a> <span class="p2">(<span class="default"><a href="rlvect_2.html#K4" title="RLVECT_2:func.4">ZeroLC</a> <font color="Maroon" title="c1">V</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="rlvect_2.html#K14" title="RLVECT_2:func.14">LCAdd</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="rlvect_2.html#K15" title="RLVECT_2:func.15">LCMult</a> <font color="Maroon" title="c1">V</font></span>)</span> #),<span class="p1">(<span class="default"><a href="rlvect_2.html#K9" title="RLVECT_2:func.9">-</a> <font color="Maroon" title="c16">K</font></span>)</span>
 <b>by </b><i><a class="ref" href="rlvect_2.html#D1" target="_self" title="RLVECT_2:def.1">Def1</a></i>;<br/><b>then </b><font color="Maroon" title="c5">v</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">+</a> <span class="p1">(<span class="default"><a href="rlvect_2.html#K1" title="RLVECT_2:func.1">vector</a> <a href="rlvect_1.html#G2" title="RLVECT_1:aggr.2">RLSStruct</a>(# <span class="p1">(<span class="default"><a href="rlvect_2.html#K11" title="RLVECT_2:func.11">LinComb</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="rlvect_2.html#K13" title="RLVECT_2:func.13">@</a> <span class="p2">(<span class="default"><a href="rlvect_2.html#K4" title="RLVECT_2:func.4">ZeroLC</a> <font color="Maroon" title="c1">V</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="rlvect_2.html#K14" title="RLVECT_2:func.14">LCAdd</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="rlvect_2.html#K15" title="RLVECT_2:func.15">LCMult</a> <font color="Maroon" title="c1">V</font></span>)</span> #),<span class="p2">(<span class="default"><a href="rlvect_2.html#K9" title="RLVECT_2:func.9">-</a> <font color="Maroon" title="c16">K</font></span>)</span></span>)</span> = 
<font color="Maroon" title="c16">K</font> <a href="rlvect_2.html#K10" title="RLVECT_2:func.10">-</a> <font color="Maroon" title="c16">K</font>
<b>by </b><i><a class="txt" href="rlvect_2.html#E4:77_1_1_1"><i><font color="Green" title="E46">A1</font></i></a></i>
<br/>.= 
 <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="rlvect_1.html#G2" title="RLVECT_1:aggr.2">RLSStruct</a>(# <span class="p1">(<span class="default"><a href="rlvect_2.html#K11" title="RLVECT_2:func.11">LinComb</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="rlvect_2.html#K13" title="RLVECT_2:func.13">@</a> <span class="p2">(<span class="default"><a href="rlvect_2.html#K4" title="RLVECT_2:func.4">ZeroLC</a> <font color="Maroon" title="c1">V</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="rlvect_2.html#K14" title="RLVECT_2:func.14">LCAdd</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="rlvect_2.html#K15" title="RLVECT_2:func.15">LCMult</a> <font color="Maroon" title="c1">V</font></span>)</span> #)
<b>by </b><i><a class="ref" href="rlvect_2.html#T82" target="_self" title="RLVECT_2:th.82">Th82</a></i>
;<br/><b>hence </b><a NAME="E13:77_1_1_1"/>
 ex <font color="Olive" title="b1">w</font> being  <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <a href="rlvect_1.html#G2" title="RLVECT_1:aggr.2">RLSStruct</a>(# <span class="p1">(<span class="default"><a href="rlvect_2.html#K11" title="RLVECT_2:func.11">LinComb</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="rlvect_2.html#K13" title="RLVECT_2:func.13">@</a> <span class="p2">(<span class="default"><a href="rlvect_2.html#K4" title="RLVECT_2:func.4">ZeroLC</a> <font color="Maroon" title="c1">V</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="rlvect_2.html#K14" title="RLVECT_2:func.14">LCAdd</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="rlvect_2.html#K15" title="RLVECT_2:func.15">LCMult</a> <font color="Maroon" title="c1">V</font></span>)</span> #) st <font color="Maroon" title="c5">v</font> <a href="rlvect_1.html#K1" title="RLVECT_1: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="rlvect_1.html#G2" title="RLVECT_1:aggr.2">RLSStruct</a>(# <span class="p1">(<span class="default"><a href="rlvect_2.html#K11" title="RLVECT_2:func.11">LinComb</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="rlvect_2.html#K13" title="RLVECT_2:func.13">@</a> <span class="p2">(<span class="default"><a href="rlvect_2.html#K4" title="RLVECT_2:func.4">ZeroLC</a> <font color="Maroon" title="c1">V</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="rlvect_2.html#K14" title="RLVECT_2:func.14">LCAdd</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="rlvect_2.html#K15" title="RLVECT_2:func.15">LCMult</a> <font color="Maroon" title="c1">V</font></span>)</span> #)
 ;<br/><b>thus </b><font color="Maroon" title="c3">a</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">+</a> <font color="Maroon" title="c7">w</font></span>)</span> = 
<font color="Maroon" title="c3">a</font> <a href="rlvect_2.html#K8" title="RLVECT_2:func.8">*</a> <font color="Maroon" title="c20">KM</font>
<b>by </b><i><a class="txt" href="rlvect_2.html#E5:77_1_1_1"><i><font color="Green" title="E47">A3</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c3">a</font> <a href="rlvect_2.html#K8" title="RLVECT_2:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c16">K</font> <a href="rlvect_2.html#K7" title="RLVECT_2:func.7">+</a> <font color="Maroon" title="c18">M</font></span>)</span>
<b>by </b><i><a class="txt" href="rlvect_2.html#E4:77_1_1_1"><i><font color="Green" title="E46">A1</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="rlvect_2.html#K8" title="RLVECT_2:func.8">*</a> <font color="Maroon" title="c16">K</font></span>)</span> <a href="rlvect_2.html#K7" title="RLVECT_2:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="rlvect_2.html#K8" title="RLVECT_2:func.8">*</a> <font color="Maroon" title="c18">M</font></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_2.html#T69" target="_self" title="RLVECT_2:th.69">Th69</a></i>
<br/>.= 
<font color="Maroon" title="c21">aK</font> <a href="rlvect_2.html#K7" title="RLVECT_2:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="rlvect_2.html#K8" title="RLVECT_2:func.8">*</a> <font color="Maroon" title="c18">M</font></span>)</span>
<b>by </b><i><a class="txt" href="rlvect_2.html#E5:77_1_1_1"><i><font color="Green" title="E47">A3</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c21">aK</font> <a href="rlvect_2.html#K7" title="RLVECT_2:func.7">+</a> <font color="Maroon" title="c22">aM</font>
<b>by </b><i><a class="txt" href="rlvect_2.html#E5:77_1_1_1"><i><font color="Green" title="E47">A3</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">*</a> <font color="Maroon" title="c5">v</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">*</a> <font color="Maroon" title="c7">w</font></span>)</span>
<b>by </b><i><a class="txt" href="rlvect_2.html#E4:77_1_1_1"><i><font color="Green" title="E46">A1</font></i></a></i>
;<br/><b>thus </b><span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c4">b</font></span>)</span> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">*</a> <font color="Maroon" title="c5">v</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c4">b</font></span>)</span> <a href="rlvect_2.html#K8" title="RLVECT_2:func.8">*</a> <font color="Maroon" title="c16">K</font>
<b>by </b><i><a class="txt" href="rlvect_2.html#E5:77_1_1_1"><i><font color="Green" title="E47">A3</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="rlvect_2.html#K8" title="RLVECT_2:func.8">*</a> <font color="Maroon" title="c16">K</font></span>)</span> <a href="rlvect_2.html#K7" title="RLVECT_2:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="rlvect_2.html#K8" title="RLVECT_2:func.8">*</a> <font color="Maroon" title="c16">K</font></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_2.html#T68" target="_self" title="RLVECT_2:th.68">Th68</a></i>
<br/>.= 
<font color="Maroon" title="c21">aK</font> <a href="rlvect_2.html#K7" title="RLVECT_2:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="rlvect_2.html#K8" title="RLVECT_2:func.8">*</a> <font color="Maroon" title="c16">K</font></span>)</span>
<b>by </b><i><a class="txt" href="rlvect_2.html#E5:77_1_1_1"><i><font color="Green" title="E47">A3</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c21">aK</font> <a href="rlvect_2.html#K7" title="RLVECT_2:func.7">+</a> <font color="Maroon" title="c23">bK</font>
<b>by </b><i><a class="txt" href="rlvect_2.html#E5:77_1_1_1"><i><font color="Green" title="E47">A3</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">*</a> <font color="Maroon" title="c5">v</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">*</a> <font color="Maroon" title="c5">v</font></span>)</span>
<b>by </b><i><a class="txt" href="rlvect_2.html#E4:77_1_1_1"><i><font color="Green" title="E46">A1</font></i></a></i>
;<br/><b>thus </b><span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <font color="Maroon" title="c4">b</font></span>)</span> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">*</a> <font color="Maroon" title="c5">v</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <font color="Maroon" title="c4">b</font></span>)</span> <a href="rlvect_2.html#K8" title="RLVECT_2:func.8">*</a> <font color="Maroon" title="c16">K</font>
<b>by </b><i><a class="txt" href="rlvect_2.html#E5:77_1_1_1"><i><font color="Green" title="E47">A3</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c3">a</font> <a href="rlvect_2.html#K8" title="RLVECT_2:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="rlvect_2.html#K8" title="RLVECT_2:func.8">*</a> <font color="Maroon" title="c16">K</font></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_2.html#T70" target="_self" title="RLVECT_2:th.70">Th70</a></i>
<br/>.= 
<font color="Maroon" title="c3">a</font> <a href="rlvect_2.html#K8" title="RLVECT_2:func.8">*</a> <font color="Maroon" title="c23">bK</font>
<b>by </b><i><a class="txt" href="rlvect_2.html#E5:77_1_1_1"><i><font color="Green" title="E47">A3</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c3">a</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">*</a> <font color="Maroon" title="c5">v</font></span>)</span>
<b>by </b><i><a class="txt" href="rlvect_2.html#E5:77_1_1_1"><i><font color="Green" title="E47">A3</font></i></a></i>
;<br/><b>thus </b>1 <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">*</a> <font color="Maroon" title="c5">v</font> = 
1 <a href="rlvect_2.html#K8" title="RLVECT_2:func.8">*</a> <font color="Maroon" title="c16">K</font>
<b>by </b><i><a class="txt" href="rlvect_2.html#E5:77_1_1_1"><i><font color="Green" title="E47">A3</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c5">v</font>
<b>by </b><i><a class="ref" href="rlvect_2.html#T71" target="_self" title="RLVECT_2:th.71">Th71</a></i>
;<br/></div><b>end;</b></div>
<a NAME="E2:77_1_1"/><b>then </b>
( ( for <font color="Olive" title="b1">v</font>, <font color="Olive" title="b2">w</font> being  <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <a href="rlvect_1.html#G2" title="RLVECT_1:aggr.2">RLSStruct</a>(# <span class="p1">(<span class="default"><a href="rlvect_2.html#K11" title="RLVECT_2:func.11">LinComb</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="rlvect_2.html#K13" title="RLVECT_2:func.13">@</a> <span class="p2">(<span class="default"><a href="rlvect_2.html#K4" title="RLVECT_2:func.4">ZeroLC</a> <font color="Maroon" title="c1">V</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="rlvect_2.html#K14" title="RLVECT_2:func.14">LCAdd</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="rlvect_2.html#K15" title="RLVECT_2:func.15">LCMult</a> <font color="Maroon" title="c1">V</font></span>)</span> #) holds  <font color="Olive" title="b1">v</font> <a href="rlvect_1.html#K1" title="RLVECT_1: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="rlvect_1.html#K1" title="RLVECT_1: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="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <a href="rlvect_1.html#G2" title="RLVECT_1:aggr.2">RLSStruct</a>(# <span class="p1">(<span class="default"><a href="rlvect_2.html#K11" title="RLVECT_2:func.11">LinComb</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="rlvect_2.html#K13" title="RLVECT_2:func.13">@</a> <span class="p2">(<span class="default"><a href="rlvect_2.html#K4" title="RLVECT_2:func.4">ZeroLC</a> <font color="Maroon" title="c1">V</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="rlvect_2.html#K14" title="RLVECT_2:func.14">LCAdd</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="rlvect_2.html#K15" title="RLVECT_2:func.15">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="rlvect_1.html#K1" title="RLVECT_1:func.1">+</a> <font color="Olive" title="b2">v</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1: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="rlvect_1.html#K1" title="RLVECT_1:func.1">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">v</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">+</a> <font color="Olive" title="b3">w</font></span>)</span> ) &amp; ( for <font color="Olive" title="b1">v</font> being  <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <a href="rlvect_1.html#G2" title="RLVECT_1:aggr.2">RLSStruct</a>(# <span class="p1">(<span class="default"><a href="rlvect_2.html#K11" title="RLVECT_2:func.11">LinComb</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="rlvect_2.html#K13" title="RLVECT_2:func.13">@</a> <span class="p2">(<span class="default"><a href="rlvect_2.html#K4" title="RLVECT_2:func.4">ZeroLC</a> <font color="Maroon" title="c1">V</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="rlvect_2.html#K14" title="RLVECT_2:func.14">LCAdd</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="rlvect_2.html#K15" title="RLVECT_2:func.15">LCMult</a> <font color="Maroon" title="c1">V</font></span>)</span> #) holds  <font color="Olive" title="b1">v</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">+</a> <span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="rlvect_1.html#G2" title="RLVECT_1:aggr.2">RLSStruct</a>(# <span class="p1">(<span class="default"><a href="rlvect_2.html#K11" title="RLVECT_2:func.11">LinComb</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="rlvect_2.html#K13" title="RLVECT_2:func.13">@</a> <span class="p2">(<span class="default"><a href="rlvect_2.html#K4" title="RLVECT_2:func.4">ZeroLC</a> <font color="Maroon" title="c1">V</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="rlvect_2.html#K14" title="RLVECT_2:func.14">LCAdd</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="rlvect_2.html#K15" title="RLVECT_2:func.15">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="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <a href="rlvect_1.html#G2" title="RLVECT_1:aggr.2">RLSStruct</a>(# <span class="p1">(<span class="default"><a href="rlvect_2.html#K11" title="RLVECT_2:func.11">LinComb</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="rlvect_2.html#K13" title="RLVECT_2:func.13">@</a> <span class="p2">(<span class="default"><a href="rlvect_2.html#K4" title="RLVECT_2:func.4">ZeroLC</a> <font color="Maroon" title="c1">V</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="rlvect_2.html#K14" title="RLVECT_2:func.14">LCAdd</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="rlvect_2.html#K15" title="RLVECT_2:func.15">LCMult</a> <font color="Maroon" title="c1">V</font></span>)</span> #)  ex <font color="Olive" title="b2">w</font> being  <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <a href="rlvect_1.html#G2" title="RLVECT_1:aggr.2">RLSStruct</a>(# <span class="p1">(<span class="default"><a href="rlvect_2.html#K11" title="RLVECT_2:func.11">LinComb</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="rlvect_2.html#K13" title="RLVECT_2:func.13">@</a> <span class="p2">(<span class="default"><a href="rlvect_2.html#K4" title="RLVECT_2:func.4">ZeroLC</a> <font color="Maroon" title="c1">V</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="rlvect_2.html#K14" title="RLVECT_2:func.14">LCAdd</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="rlvect_2.html#K15" title="RLVECT_2:func.15">LCMult</a> <font color="Maroon" title="c1">V</font></span>)</span> #) st <font color="Olive" title="b1">v</font> <a href="rlvect_1.html#K1" title="RLVECT_1: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="rlvect_1.html#G2" title="RLVECT_1:aggr.2">RLSStruct</a>(# <span class="p1">(<span class="default"><a href="rlvect_2.html#K11" title="RLVECT_2:func.11">LinComb</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="rlvect_2.html#K13" title="RLVECT_2:func.13">@</a> <span class="p2">(<span class="default"><a href="rlvect_2.html#K4" title="RLVECT_2:func.4">ZeroLC</a> <font color="Maroon" title="c1">V</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="rlvect_2.html#K14" title="RLVECT_2:func.14">LCAdd</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="rlvect_2.html#K15" title="RLVECT_2:func.15">LCMult</a> <font color="Maroon" title="c1">V</font></span>)</span> #) ) &amp; ( for <font color="Olive" title="b1">a</font> being  <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a><br/> for <font color="Olive" title="b2">v</font>, <font color="Olive" title="b3">w</font> being  <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <a href="rlvect_1.html#G2" title="RLVECT_1:aggr.2">RLSStruct</a>(# <span class="p1">(<span class="default"><a href="rlvect_2.html#K11" title="RLVECT_2:func.11">LinComb</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="rlvect_2.html#K13" title="RLVECT_2:func.13">@</a> <span class="p2">(<span class="default"><a href="rlvect_2.html#K4" title="RLVECT_2:func.4">ZeroLC</a> <font color="Maroon" title="c1">V</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="rlvect_2.html#K14" title="RLVECT_2:func.14">LCAdd</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="rlvect_2.html#K15" title="RLVECT_2:func.15">LCMult</a> <font color="Maroon" title="c1">V</font></span>)</span> #) holds  <font color="Olive" title="b1">a</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">v</font> <a href="rlvect_1.html#K1" title="RLVECT_1: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="rlvect_1.html#K2" title="RLVECT_1:func.2">*</a> <font color="Olive" title="b2">v</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">a</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">*</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="real_1.html#NM1" title="REAL_1:NM.1">Real</a><br/> for <font color="Olive" title="b3">v</font> being  <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <a href="rlvect_1.html#G2" title="RLVECT_1:aggr.2">RLSStruct</a>(# <span class="p1">(<span class="default"><a href="rlvect_2.html#K11" title="RLVECT_2:func.11">LinComb</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="rlvect_2.html#K13" title="RLVECT_2:func.13">@</a> <span class="p2">(<span class="default"><a href="rlvect_2.html#K4" title="RLVECT_2:func.4">ZeroLC</a> <font color="Maroon" title="c1">V</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="rlvect_2.html#K14" title="RLVECT_2:func.14">LCAdd</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="rlvect_2.html#K15" title="RLVECT_2:func.15">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="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Olive" title="b2">b</font></span>)</span> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">*</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="rlvect_1.html#K2" title="RLVECT_1:func.2">*</a> <font color="Olive" title="b3">v</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">b</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">*</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="real_1.html#NM1" title="REAL_1:NM.1">Real</a><br/> for <font color="Olive" title="b3">v</font> being  <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <a href="rlvect_1.html#G2" title="RLVECT_1:aggr.2">RLSStruct</a>(# <span class="p1">(<span class="default"><a href="rlvect_2.html#K11" title="RLVECT_2:func.11">LinComb</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="rlvect_2.html#K13" title="RLVECT_2:func.13">@</a> <span class="p2">(<span class="default"><a href="rlvect_2.html#K4" title="RLVECT_2:func.4">ZeroLC</a> <font color="Maroon" title="c1">V</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="rlvect_2.html#K14" title="RLVECT_2:func.14">LCAdd</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="rlvect_2.html#K15" title="RLVECT_2:func.15">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="real_1.html#K4" title="REAL_1:func.4">*</a> <font color="Olive" title="b2">b</font></span>)</span> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">*</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="rlvect_1.html#K2" title="RLVECT_1:func.2">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">b</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">*</a> <font color="Olive" title="b3">v</font></span>)</span> ) &amp; ( for <font color="Olive" title="b1">v</font> being  <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <a href="rlvect_1.html#G2" title="RLVECT_1:aggr.2">RLSStruct</a>(# <span class="p1">(<span class="default"><a href="rlvect_2.html#K11" title="RLVECT_2:func.11">LinComb</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="rlvect_2.html#K13" title="RLVECT_2:func.13">@</a> <span class="p2">(<span class="default"><a href="rlvect_2.html#K4" title="RLVECT_2:func.4">ZeroLC</a> <font color="Maroon" title="c1">V</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="rlvect_2.html#K14" title="RLVECT_2:func.14">LCAdd</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="rlvect_2.html#K15" title="RLVECT_2:func.15">LCMult</a> <font color="Maroon" title="c1">V</font></span>)</span> #) holds  1 <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">*</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/>
<b>hence </b><a NAME="E3:77_1_1"/>
 <a href="rlvect_1.html#G2" title="RLVECT_1:aggr.2">RLSStruct</a>(# <span class="p1">(<span class="default"><a href="rlvect_2.html#K11" title="RLVECT_2:func.11">LinComb</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="rlvect_2.html#K13" title="RLVECT_2:func.13">@</a> <span class="p2">(<span class="default"><a href="rlvect_2.html#K4" title="RLVECT_2:func.4">ZeroLC</a> <font color="Maroon" title="c1">V</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="rlvect_2.html#K14" title="RLVECT_2:func.14">LCAdd</a> <font color="Maroon" title="c1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="rlvect_2.html#K15" title="RLVECT_2:func.15">LCMult</a> <font color="Maroon" title="c1">V</font></span>)</span> #) is   <a href="rlvect_1.html#NM2" title="RLVECT_1:NM.2">RealLinearSpace</a>
 <b>by </b><i><a class="ref" href="rlvect_1.html#T7" title="RLVECT_1:th.7">RLVECT_1:7</a></i>;<br/>


</div>
