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

<b>let </b><font color="Maroon" title="c1">a</font> be   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>;<br/><b>let </b><font color="Maroon" title="c2">V</font> be   <a href="rlvect_1.html#NM2" title="RLVECT_1:NM.2">RealLinearSpace</a>;<br/><b>let </b><font color="Maroon" title="c3">v</font>, <font color="Maroon" title="c4">w</font> be   <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c2">V</font>;<br/>







<b>assume </b><b>that </b><br/><a NAME="E1:48"/><i><font color="Green" title="E29">A1</font></i>: 
<font color="Maroon" title="c1">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> 
 <b>and </b><br/><a NAME="E2:48"/><i><font color="Green" title="E30">A2</font></i>: 
<font color="Maroon" title="c1">a</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">*</a> <font color="Maroon" title="c3">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">a</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">*</a> <font color="Maroon" title="c4">w</font>
 ;<br/>

 <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">V</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">*</a> <font color="Maroon" title="c3">v</font></span>)</span> <a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">*</a> <font color="Maroon" title="c4">w</font></span>)</span>
<b>by </b><i><a class="txt" href="rlvect_1.html#E2:48"><i><font color="Green" title="E30">A2</font></i></a>, <a class="ref" href="rlvect_1.html#D10" target="_self" title="RLVECT_1:def.10">Def10</a></i>
<br/>.= 
<font color="Maroon" title="c1">a</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">v</font> <a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <font color="Maroon" title="c4">w</font></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#T48" target="_self" title="RLVECT_1:th.48">Th48</a></i>
;<br/>
<a NAME="E4:48"/><b>then </b>
<font color="Maroon" title="c3">v</font> <a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <font color="Maroon" title="c4">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> <font color="Maroon" title="c2">V</font>
 
<b>by </b><i><a class="txt" href="rlvect_1.html#E1:48"><i><font color="Green" title="E29">A1</font></i></a>, <a class="ref" href="rlvect_1.html#T24" target="_self" title="RLVECT_1:th.24">Th24</a></i>;<br/>
<b>hence </b><a NAME="E5:48"/>
<font color="Maroon" title="c3">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">w</font>
 <b>by </b><i><a class="ref" href="rlvect_1.html#T35" target="_self" title="RLVECT_1:th.35">Th35</a></i>;<br/>


</div>
