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<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">p</font>, <font color="Maroon" title="c3">v</font>, <font color="Maroon" title="c4">w</font>, <font color="Maroon" title="c5">u</font> be   <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font>;<br/>









<b>assume </b><b>that </b><br/><a NAME="E1:18"/><i><font color="Green" title="E22">A1</font></i>: 
<font color="Maroon" title="c2">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">v</font>
 <b>and </b><br/><a NAME="E2:18"/><i><font color="Green" title="E23">A2</font></i>: 
<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c2">p</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c4">w</font>
 ;<br/>

<div><i><font color="Green" title="E24">A3</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="18_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:18_1"/><i><font color="Green" title="E25">A4</font></i>: 
<font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">w</font>
 ;<br/><b>take </b><font color="Maroon" title="c6">y</font> = <font color="Maroon" title="c2">p</font>;<br/><b>thus </b><a NAME="E2:18_1"/>
( <font color="Maroon" title="c5">u</font>,<font color="Maroon" title="c2">p</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c6">y</font> &amp; <font color="Maroon" title="c5">u</font>,<font color="Maroon" title="c3">v</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c4">w</font>,<font color="Maroon" title="c6">y</font> )
 <b>by </b><i><a class="txt" href="analoaf.html#E1:18_1"><i><font color="Green" title="E25">A4</font></i></a>, <a class="ref" href="analoaf.html#D1" target="_self" title="ANALOAF:def.1">Def1</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="18_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:18_2"/>
<font color="Maroon" title="c2">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">w</font>
 ;<br/><b>then consider </b><font color="Maroon" title="c6">a</font>, <font color="Maroon" title="c7">b</font> being   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a><b> such that </b><br/><a NAME="E3:18_2"/><i><font color="Green" title="E25">A5</font></i>: 
( <font color="Maroon" title="c6">a</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <font color="Maroon" title="c3">v</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">b</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">w</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <font color="Maroon" title="c2">p</font></span>)</span> &amp; 0 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <font color="Maroon" title="c6">a</font> &amp; 0 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <font color="Maroon" title="c7">b</font> )
 <b>by </b><i><a class="txt" href="analoaf.html#E1:18"><i><font color="Green" title="E22">A1</font></i></a>, <a class="txt" href="analoaf.html#E2:18"><i><font color="Green" title="E23">A2</font></i></a>, <a class="ref" href="analoaf.html#T16" target="_self" title="ANALOAF:th.16">Th16</a></i>;<br/><b>set </b><font color="Maroon" title="c8">y</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c7">b</font> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <font color="Maroon" title="c6">a</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="c2">p</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <font color="Maroon" title="c5">u</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">+</a> <font color="Maroon" title="c2">p</font>;<br/><i><font color="Green" title="E26">A6</font></i>: 1 <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c7">b</font> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <font color="Maroon" title="c6">a</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <font color="Maroon" title="c5">u</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">+</a> <font color="Maroon" title="c2">p</font></span>)</span> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <font color="Maroon" title="c2">p</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">b</font> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <font color="Maroon" title="c6">a</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <font color="Maroon" title="c5">u</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">+</a> <font color="Maroon" title="c2">p</font></span>)</span> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <font color="Maroon" title="c2">p</font>
<b>by </b><i><a class="ref" href="rlvect_1.html#D9" title="RLVECT_1:def.9">RLVECT_1:def 9</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">b</font> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <font color="Maroon" title="c6">a</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="c2">p</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <font color="Maroon" title="c5">u</font></span>)</span>
<b>by </b><i><a class="ref" href="rlsub_2.html#T78" title="RLSUB_2:th.78">RLSUB_2:78</a></i>
;<br/><a NAME="E5:18_2"/>
0 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <font color="Maroon" title="c7">b</font> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> 
 <b>by </b><i><a class="txt" href="analoaf.html#E3:18_2"><i><font color="Green" title="E25">A5</font></i></a>, <a class="ref" href="xreal_1.html#T124" title="XREAL_1:th.124">XREAL_1:124</a></i>;<br/><a NAME="E6:18_2"/><b>then </b>
( 0 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">b</font> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <font color="Maroon" title="c6">a</font> &amp; 0 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> 1 )
 <b>by </b><i><a class="txt" href="analoaf.html#E3:18_2"><i><font color="Green" title="E25">A5</font></i></a>, <a class="ref" href="xreal_1.html#T131" title="XREAL_1:th.131">XREAL_1:131</a></i>;<br/><a NAME="E7:18_2"/><b>then </b><i><font color="Green" title="E27">A7</font></i>: 
<font color="Maroon" title="c5">u</font>,<font color="Maroon" title="c2">p</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c2">p</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c7">b</font> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <font color="Maroon" title="c6">a</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="c2">p</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <font color="Maroon" title="c5">u</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">+</a> <font color="Maroon" title="c2">p</font>
 <b>by </b><i><a class="txt" href="analoaf.html#E4:18_2"><i><font color="Green" title="E26">A6</font></i></a>, <a class="ref" href="analoaf.html#D1" target="_self" title="ANALOAF:def.1">Def1</a></i>;<br/><i><font color="Green" title="E28">A8</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">b</font> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <font color="Maroon" title="c6">a</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <font color="Maroon" title="c5">u</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">+</a> <font color="Maroon" title="c2">p</font></span>)</span> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <font color="Maroon" title="c2">p</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">b</font> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <font color="Maroon" title="c6">a</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="c2">p</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <font color="Maroon" title="c5">u</font></span>)</span>
<b>by </b><i><a class="ref" href="rlsub_2.html#T78" title="RLSUB_2:th.78">RLSUB_2:78</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c7">b</font> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </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">a</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <font color="Maroon" title="c5">u</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#D9" title="RLVECT_1:def.9">RLVECT_1:def 9</a></i>
;<br/><i><font color="Green" title="E29">A9</font></i>: <font color="Maroon" title="c3">v</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <font color="Maroon" title="c5">u</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <font color="Maroon" title="c5">u</font></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">v</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <font color="Maroon" title="c2">p</font></span>)</span>
<b>by </b><i><a class="ref" href="analoaf.html#T4" target="_self" title="ANALOAF:th.4">Th4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <font color="Maroon" title="c5">u</font></span>)</span> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <font color="Maroon" title="c3">v</font></span>)</span>
<b>by </b><i><a class="txt" href="analoaf.html#E8"><i><font color="Green" title="E5">Lm3</font></i></a></i>
;<br/><i><font color="Green" title="E30">A10</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">b</font> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <font color="Maroon" title="c6">a</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <font color="Maroon" title="c5">u</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">+</a> <font color="Maroon" title="c2">p</font></span>)</span> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <font color="Maroon" title="c4">w</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c7">b</font> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <font color="Maroon" title="c6">a</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <font color="Maroon" title="c5">u</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">+</a> <font color="Maroon" title="c2">p</font></span>)</span> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <font color="Maroon" title="c2">p</font></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <font color="Maroon" title="c4">w</font></span>)</span>
<b>by </b><i><a class="ref" href="analoaf.html#T4" target="_self" title="ANALOAF:th.4">Th4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c7">b</font> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <font color="Maroon" title="c6">a</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <font color="Maroon" title="c5">u</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">+</a> <font color="Maroon" title="c2">p</font></span>)</span> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <font color="Maroon" title="c2">p</font></span>)</span> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">w</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <font color="Maroon" title="c2">p</font></span>)</span>
<b>by </b><i><a class="txt" href="analoaf.html#E8"><i><font color="Green" title="E5">Lm3</font></i></a></i>
;<br/><font color="Maroon" title="c6">a</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">v</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <font color="Maroon" title="c5">u</font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">a</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <font color="Maroon" title="c5">u</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">a</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <font color="Maroon" title="c3">v</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="analoaf.html#E9:18_2"><i><font color="Green" title="E29">A9</font></i></a>, <a class="ref" href="rlvect_1.html#T48" title="RLVECT_1:th.48">RLVECT_1:48</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c7">b</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c7">b</font> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <font color="Maroon" title="c6">a</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <font color="Maroon" title="c5">u</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">+</a> <font color="Maroon" title="c2">p</font></span>)</span> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <font color="Maroon" title="c2">p</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">b</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">w</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <font color="Maroon" title="c2">p</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="analoaf.html#E3:18_2"><i><font color="Green" title="E25">A5</font></i></a>, <a class="txt" href="analoaf.html#E8:18_2"><i><font color="Green" title="E28">A8</font></i></a>, <a class="ref" href="analoaf.html#T13" target="_self" title="ANALOAF:th.13">Th13</a></i>
<br/>.= 
<font color="Maroon" title="c7">b</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c7">b</font> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <font color="Maroon" title="c6">a</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <font color="Maroon" title="c5">u</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">+</a> <font color="Maroon" title="c2">p</font></span>)</span> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <font color="Maroon" title="c4">w</font></span>)</span>
<b>by </b><i><a class="txt" href="analoaf.html#E10:18_2"><i><font color="Green" title="E30">A10</font></i></a>, <a class="ref" href="rlvect_1.html#T48" title="RLVECT_1:th.48">RLVECT_1:48</a></i>
;<br/><a NAME="E12:18_2"/><b>then </b>
<font color="Maroon" title="c5">u</font>,<font color="Maroon" title="c3">v</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c4">w</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c7">b</font> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <font color="Maroon" title="c6">a</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="c2">p</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <font color="Maroon" title="c5">u</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">+</a> <font color="Maroon" title="c2">p</font>
 <b>by </b><i><a class="txt" href="analoaf.html#E3:18_2"><i><font color="Green" title="E25">A5</font></i></a>, <a class="ref" href="analoaf.html#D1" target="_self" title="ANALOAF:def.1">Def1</a></i>;<br/><b>hence </b><a NAME="E13:18_2"/>
 ex <font color="Olive" title="b1">y</font> being  <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font> st <br/>( <font color="Maroon" title="c5">u</font>,<font color="Maroon" title="c2">p</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c2">p</font>,<font color="Olive" title="b1">y</font> &amp; <font color="Maroon" title="c5">u</font>,<font color="Maroon" title="c3">v</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c4">w</font>,<font color="Olive" title="b1">y</font> )
 <b>by </b><i><a class="txt" href="analoaf.html#E7:18_2"><i><font color="Green" title="E27">A7</font></i></a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:18"/>
 ex <font color="Olive" title="b1">y</font> being  <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font> st <br/>( <font color="Maroon" title="c5">u</font>,<font color="Maroon" title="c2">p</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c2">p</font>,<font color="Olive" title="b1">y</font> &amp; <font color="Maroon" title="c5">u</font>,<font color="Maroon" title="c3">v</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c4">w</font>,<font color="Olive" title="b1">y</font> )
 <b>by </b><i><a class="txt" href="analoaf.html#E3:18"><i><font color="Green" title="E24">A3</font></i></a></i>;<br/>


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