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

<b>let </b><font color="Maroon" title="c1">V</font> be   <a href="rlvect_1.html#NM2" title="RLVECT_1:NM.2">RealLinearSpace</a>;<br/><b>let </b><font color="Maroon" title="c2">v</font>, <font color="Maroon" title="c3">w</font>, <font color="Maroon" title="c4">u</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">V</font>;<br/>







<b>assume </b><b>that </b><br/><a NAME="E1:11"/><i><font color="Green" title="E11">A1</font></i>: 
( <font color="Maroon" title="c2">v</font> <a href="anproj_1.html#NR1" title="ANPROJ_1:NR.1">is_Prop_Vect</a>  &amp; <font color="Maroon" title="c3">w</font> <a href="anproj_1.html#NR1" title="ANPROJ_1:NR.1">is_Prop_Vect</a>  )
 <b>and </b><br/><a NAME="E2:11"/><i><font color="Green" title="E12">A2</font></i>: 
not  <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">w</font>
 ;<br/>

<a NAME="E3:11"/><i><font color="Green" title="E13">A3</font></i>: 
( <font color="Maroon" title="c2">v</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">V</font> &amp; <font color="Maroon" title="c3">w</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">V</font> )
 
<b>by </b><i><a class="txt" href="anproj_1.html#E1:11"><i><font color="Green" title="E11">A1</font></i></a>, <a class="ref" href="rlvect_1.html#D13" title="RLVECT_1:def.13">RLVECT_1:def 13</a></i>;<br/>
<a NAME="E4:11"/><i><font color="Green" title="E14">A4</font></i>: 
( <font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">w</font>,<font color="Maroon" title="c4">u</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a>  implies  ex <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> st <font color="Maroon" title="c4">u</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="Maroon" title="c2">v</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</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="Maroon" title="c3">w</font></span>)</span> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="11_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:11_1"/>
<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">w</font>,<font color="Maroon" title="c4">u</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a> 
 ;<br/>

<a NAME="E2:11_1"/><b>then </b>
<font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">w</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a> 
 
<b>by </b><i><a class="ref" href="anproj_1.html#T10" target="_self" title="ANPROJ_1:th.10">Th10</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c5">a</font>, <font color="Maroon" title="c6">b</font>, <font color="Maroon" title="c7">c</font> being   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a><b> such that </b><br/><a NAME="E4:11_1"/><i><font color="Green" title="E15">A5</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">a</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">*</a> <font color="Maroon" title="c4">u</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">b</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">*</a> <font color="Maroon" title="c2">v</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">c</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">*</a> <font color="Maroon" title="c3">w</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">V</font>
 <b>and </b><br/><a NAME="E5:11_1"/><i><font color="Green" title="E16">A6</font></i>: 
( <font color="Maroon" title="c5">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or <font color="Maroon" title="c6">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or <font color="Maroon" title="c7">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 <b>by </b><i><a class="ref" href="anproj_1.html#D3" target="_self" title="ANPROJ_1:def.3">Def3</a></i>;<br/>
<a NAME="E6:11_1"/>
<font color="Maroon" title="c5">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="11_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:11_1_1"/><i><font color="Green" title="E17">A7</font></i>: 
<font color="Maroon" title="c5">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ;<br/>

<b>then </b><i><font color="Green" title="E18">A8</font></i>:  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">V</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">V</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">b</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">*</a> <font color="Maroon" title="c2">v</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">c</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">*</a> <font color="Maroon" title="c3">w</font></span>)</span>
<b>by </b><i><a class="txt" href="anproj_1.html#E4:11_1"><i><font color="Green" title="E15">A5</font></i></a>, <a class="ref" href="rlvect_1.html#T23" title="RLVECT_1:th.23">RLVECT_1:23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">b</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">*</a> <font color="Maroon" title="c2">v</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">c</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">*</a> <font color="Maroon" title="c3">w</font></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#T10" title="RLVECT_1:th.10">RLVECT_1:10</a></i>
;<br/>
<a NAME="E3:11_1_1"/><b>then </b>
<font color="Maroon" title="c6">b</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">*</a> <font color="Maroon" title="c2">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">c</font></span>)</span> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">*</a> <font color="Maroon" title="c3">w</font>
 
<b>by </b><i><a class="txt" href="anproj_1.html#E14"><i><font color="Green" title="E8">Lm1</font></i></a></i>;<br/>
<a NAME="E4:11_1_1"/><b>then </b><i><font color="Green" title="E19">A9</font></i>: 
( <font color="Maroon" title="c6">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or  <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 
<b>by </b><i><a class="txt" href="anproj_1.html#E2:11"><i><font color="Green" title="E12">A2</font></i></a>, <a class="ref" href="anproj_1.html#D2" target="_self" title="ANPROJ_1:def.2">Def2</a></i>;<br/>
<a NAME="E5:11_1_1"/><i><font color="Green" title="E20">A10</font></i>: 
<font color="Maroon" title="c6">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="11_1_1_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:11_1_1_2"/><i><font color="Green" title="E21">A11</font></i>: 
<font color="Maroon" title="c6">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ;<br/>

<b>then </b> <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">V</font> = 
<span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">V</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">c</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">*</a> <font color="Maroon" title="c3">w</font></span>)</span>
<b>by </b><i><a class="txt" href="anproj_1.html#E2:11_1_1"><i><font color="Green" title="E18">A8</font></i></a>, <a class="ref" href="rlvect_1.html#T23" title="RLVECT_1:th.23">RLVECT_1:23</a></i>
<br/>.= 
<font color="Maroon" title="c7">c</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">*</a> <font color="Maroon" title="c3">w</font>
<b>by </b><i><a class="ref" href="rlvect_1.html#T10" title="RLVECT_1:th.10">RLVECT_1:10</a></i>
;<br/>
<b>hence </b><a NAME="E3:11_1_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="anproj_1.html#E3:11"><i><font color="Green" title="E13">A3</font></i></a>, <a class="txt" href="anproj_1.html#E5:11_1"><i><font color="Green" title="E16">A6</font></i></a>, <a class="txt" href="anproj_1.html#E1:11_1_1"><i><font color="Green" title="E17">A7</font></i></a>, <a class="txt" href="anproj_1.html#E1:11_1_1_2"><i><font color="Green" title="E21">A11</font></i></a>, <a class="ref" href="rlvect_1.html#T24" title="RLVECT_1:th.24">RLVECT_1:24</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E6:11_1_1"/>
<font color="Maroon" title="c7">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="11_1_1_3"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:11_1_1_3"/><i><font color="Green" title="E21">A12</font></i>: 
<font color="Maroon" title="c7">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ;<br/>

<b>then </b> <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">V</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">b</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">*</a> <font color="Maroon" title="c2">v</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">V</font></span>)</span>
<b>by </b><i><a class="txt" href="anproj_1.html#E2:11_1_1"><i><font color="Green" title="E18">A8</font></i></a>, <a class="ref" href="rlvect_1.html#T23" title="RLVECT_1:th.23">RLVECT_1:23</a></i>
<br/>.= 
<font color="Maroon" title="c6">b</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">*</a> <font color="Maroon" title="c2">v</font>
<b>by </b><i><a class="ref" href="rlvect_1.html#T10" title="RLVECT_1:th.10">RLVECT_1:10</a></i>
;<br/>
<b>hence </b><a NAME="E3:11_1_1_3"/>
contradiction
 <b>by </b><i><a class="txt" href="anproj_1.html#E3:11"><i><font color="Green" title="E13">A3</font></i></a>, <a class="txt" href="anproj_1.html#E5:11_1"><i><font color="Green" title="E16">A6</font></i></a>, <a class="txt" href="anproj_1.html#E1:11_1_1"><i><font color="Green" title="E17">A7</font></i></a>, <a class="txt" href="anproj_1.html#E1:11_1_1_3"><i><font color="Green" title="E21">A12</font></i></a>, <a class="ref" href="rlvect_1.html#T24" title="RLVECT_1:th.24">RLVECT_1:24</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E7:11_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="anproj_1.html#E4:11_1_1"><i><font color="Green" title="E19">A9</font></i></a>, <a class="txt" href="anproj_1.html#E5:11_1_1"><i><font color="Green" title="E20">A10</font></i></a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E7:11_1"/><b>then </b>
<font color="Maroon" title="c4">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c5">a</font> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c6">b</font></span>)</span></span>)</span> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">*</a> <font color="Maroon" title="c2">v</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c5">a</font> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c7">c</font></span>)</span></span>)</span> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">*</a> <font color="Maroon" title="c3">w</font></span>)</span>
 
<b>by </b><i><a class="txt" href="anproj_1.html#E4:11_1"><i><font color="Green" title="E15">A5</font></i></a>, <a class="txt" href="anproj_1.html#E15"><i><font color="Green" title="E9">Lm2</font></i></a></i>;<br/>
<b>hence </b><a NAME="E8:11_1"/>
 ex <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> st <font color="Maroon" title="c4">u</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="Maroon" title="c2">v</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</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="Maroon" title="c3">w</font></span>)</span>
 ;<br/>


</div><b>end;</b></div>
<a NAME="E5:11"/>
(  ex <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> st <font color="Maroon" title="c4">u</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="Maroon" title="c2">v</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</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="Maroon" title="c3">w</font></span>)</span> implies <font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">w</font>,<font color="Maroon" title="c4">u</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a>  )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="11_2"><b>proof </b></a><div class="add">

<b>given </b><font color="Maroon" title="c5">a</font>, <font color="Maroon" title="c6">b</font> being   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a><b> such that </b><a NAME="E2:11_2"/><i><font color="Green" title="E15">A13</font></i>: 
<font color="Maroon" title="c4">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">a</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">*</a> <font color="Maroon" title="c2">v</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">b</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">*</a> <font color="Maroon" title="c3">w</font></span>)</span>
 ;<br/>

 <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">V</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">a</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">*</a> <font color="Maroon" title="c2">v</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">b</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">*</a> <font color="Maroon" title="c3">w</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c4">u</font></span>)</span>
<b>by </b><i><a class="txt" href="anproj_1.html#E2:11_2"><i><font color="Green" title="E15">A13</font></i></a>, <a class="ref" href="rlvect_1.html#T16" title="RLVECT_1:th.16">RLVECT_1:16</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">a</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">*</a> <font color="Maroon" title="c2">v</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">b</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">*</a> <font color="Maroon" title="c3">w</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">*</a> <font color="Maroon" title="c4">u</font></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#T29" title="RLVECT_1:th.29">RLVECT_1:29</a></i>
;<br/>
<b>hence </b><a NAME="E4:11_2"/>
<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">w</font>,<font color="Maroon" title="c4">u</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a> 
 <b>by </b><i><a class="ref" href="anproj_1.html#D3" target="_self" title="ANPROJ_1:def.3">Def3</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E6:11"/>
( <font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">w</font>,<font color="Maroon" title="c4">u</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a>  iff  ex <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> st <font color="Maroon" title="c4">u</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="Maroon" title="c2">v</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</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="Maroon" title="c3">w</font></span>)</span> )
 <b>by </b><i><a class="txt" href="anproj_1.html#E4:11"><i><font color="Green" title="E14">A4</font></i></a></i>;<br/>


</div>
