<?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">w</font>, <font color="Maroon" title="c3">y</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>let </b><font color="Maroon" title="c4">u</font>, <font color="Maroon" title="c5">u1</font>, <font color="Maroon" title="c6">u2</font>, <font color="Maroon" title="c7">v1</font>, <font color="Maroon" title="c8">v2</font>, <font color="Maroon" title="c9">t1</font>, <font color="Maroon" title="c10">t2</font>, <font color="Maroon" title="c11">w1</font>, <font color="Maroon" title="c12">w2</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="E1:41"/><i><font color="Green" title="E39">A1</font></i>: 
 <a href="analmetr.html#R1" title="ANALMETR:pred.1">Gen</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>
 <b>and </b><br/><a NAME="E2:41"/><i><font color="Green" title="E40">A2</font></i>: 
( <font color="Maroon" title="c4">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">u1</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c9">t1</font> &amp; <font color="Maroon" title="c4">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">u2</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c10">t2</font> &amp; <font color="Maroon" title="c4">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">v1</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c11">w1</font> &amp; <font color="Maroon" title="c4">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">v2</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c12">w2</font> )
 <b>and </b><br/><a NAME="E3:41"/><i><font color="Green" title="E41">A3</font></i>: 
<font color="Maroon" title="c5">u1</font>,<font color="Maroon" title="c6">u2</font>,<font color="Maroon" title="c7">v1</font>,<font color="Maroon" title="c8">v2</font> <a href="geomtrap.html#R2" title="GEOMTRAP:pred.2">are_DTr_wrt</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>
 ;<br/>

<b>set </b><font color="Maroon" title="c13">p</font> = <font color="Maroon" title="c5">u1</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c6">u2</font>;<br/>
<b>set </b><font color="Maroon" title="c14">q</font> = <font color="Maroon" title="c7">v1</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c8">v2</font>;<br/>
<b>set </b><font color="Maroon" title="c15">r</font> = <font color="Maroon" title="c9">t1</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c10">t2</font>;<br/>
<b>set </b><font color="Maroon" title="c16">s</font> = <font color="Maroon" title="c11">w1</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c12">w2</font>;<br/>
<a NAME="E4:41"/><i><font color="Green" title="E42">A4</font></i>: 
( <font color="Maroon" title="c5">u1</font>,<font color="Maroon" title="c6">u2</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c7">v1</font>,<font color="Maroon" title="c8">v2</font> &amp; <font color="Maroon" title="c5">u1</font>,<font color="Maroon" title="c6">u2</font>,<font color="Maroon" title="c5">u1</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c6">u2</font>,<font color="Maroon" title="c7">v1</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c8">v2</font> <a href="analmetr.html#R3" title="ANALMETR:pred.3">are_Ort_wrt</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font> &amp; <font color="Maroon" title="c7">v1</font>,<font color="Maroon" title="c8">v2</font>,<font color="Maroon" title="c5">u1</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c6">u2</font>,<font color="Maroon" title="c7">v1</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c8">v2</font> <a href="analmetr.html#R3" title="ANALMETR:pred.3">are_Ort_wrt</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font> )
 
<b>by </b><i><a class="txt" href="geomtrap.html#E3:41"><i><font color="Green" title="E41">A3</font></i></a>, <a class="ref" href="geomtrap.html#D3" target="_self" title="GEOMTRAP:def.3">Def3</a></i>;<br/>
<a NAME="E5:41"/><i><font color="Green" title="E43">A5</font></i>: 
( <font color="Maroon" title="c6">u2</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <font color="Maroon" title="c5">u1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">t2</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <font color="Maroon" title="c9">t1</font></span>)</span> &amp; <font color="Maroon" title="c8">v2</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <font color="Maroon" title="c7">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">w2</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <font color="Maroon" title="c11">w1</font></span>)</span> )
 
<b>by </b><i><a class="txt" href="geomtrap.html#E2:41"><i><font color="Green" title="E40">A2</font></i></a>, <a class="txt" href="geomtrap.html#E21"><i><font color="Green" title="E18">Lm3</font></i></a></i>;<br/>
<div><i><font color="Green" title="E44">A6</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="41_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:41_1"/>
<font color="Maroon" title="c5">u1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">u2</font>
 ;<br/><a NAME="E2:41_1"/><b>then </b>
<font color="Maroon" title="c9">t1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">t2</font>
 <b>by </b><i><a class="txt" href="geomtrap.html#E2:41"><i><font color="Green" title="E40">A2</font></i></a>, <a class="ref" href="geomtrap.html#T9" target="_self" title="GEOMTRAP:th.9">Th9</a></i>;<br/><b>hence </b><a NAME="E3:41_1"/>
( <font color="Maroon" title="c9">t1</font>,<font color="Maroon" title="c10">t2</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c11">w1</font>,<font color="Maroon" title="c12">w2</font> &amp; <font color="Maroon" title="c9">t1</font>,<font color="Maroon" title="c10">t2</font>,<font color="Maroon" title="c9">t1</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c10">t2</font>,<font color="Maroon" title="c11">w1</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c12">w2</font> <a href="analmetr.html#R3" title="ANALMETR:pred.3">are_Ort_wrt</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font> )
 <b>by </b><i><a class="txt" href="geomtrap.html#E1:41"><i><font color="Green" title="E39">A1</font></i></a>, <a class="txt" href="geomtrap.html#E26"><i><font color="Green" title="E23">Lm8</font></i></a>, <a class="ref" href="analoaf.html#T18" title="ANALOAF:th.18">ANALOAF:18</a></i>;<br/></div><b>end;</b></div>
<div><i><font color="Green" title="E45">A7</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="41_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:41_2"/>
<font color="Maroon" title="c7">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">v2</font>
 ;<br/><a NAME="E2:41_2"/><b>then </b>
<font color="Maroon" title="c11">w1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">w2</font>
 <b>by </b><i><a class="txt" href="geomtrap.html#E2:41"><i><font color="Green" title="E40">A2</font></i></a>, <a class="ref" href="geomtrap.html#T9" target="_self" title="GEOMTRAP:th.9">Th9</a></i>;<br/><b>hence </b><a NAME="E3:41_2"/>
( <font color="Maroon" title="c9">t1</font>,<font color="Maroon" title="c10">t2</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c11">w1</font>,<font color="Maroon" title="c12">w2</font> &amp; <font color="Maroon" title="c11">w1</font>,<font color="Maroon" title="c12">w2</font>,<font color="Maroon" title="c9">t1</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c10">t2</font>,<font color="Maroon" title="c11">w1</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c12">w2</font> <a href="analmetr.html#R3" title="ANALMETR:pred.3">are_Ort_wrt</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font> )
 <b>by </b><i><a class="txt" href="geomtrap.html#E1:41"><i><font color="Green" title="E39">A1</font></i></a>, <a class="txt" href="geomtrap.html#E26"><i><font color="Green" title="E23">Lm8</font></i></a>, <a class="ref" href="analoaf.html#T18" title="ANALOAF:th.18">ANALOAF:18</a></i>;<br/></div><b>end;</b></div>
<a NAME="E8:41"/><i><font color="Green" title="E46">A8</font></i>: 
<font color="Maroon" title="c9">t1</font>,<font color="Maroon" title="c10">t2</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c11">w1</font>,<font color="Maroon" title="c12">w2</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="41_3"><b>proof </b></a><div class="add">

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="41_3_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:41_3_1"/>
( <font color="Maroon" title="c5">u1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">u2</font> &amp; <font color="Maroon" title="c7">v1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">v2</font> )
 ;<br/><b>then consider </b><font color="Maroon" title="c17">a</font>, <font color="Maroon" title="c18">b</font> being   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a><b> such that </b><br/><a NAME="E3:41_3_1"/><i><font color="Green" title="E47">A9</font></i>: 
( 0 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <font color="Maroon" title="c17">a</font> &amp; 0 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <font color="Maroon" title="c18">b</font> &amp; <font color="Maroon" title="c17">a</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">u2</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <font color="Maroon" title="c5">u1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">b</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <font color="Maroon" title="c7">v1</font></span>)</span> )
 <b>by </b><i><a class="txt" href="geomtrap.html#E4:41"><i><font color="Green" title="E42">A4</font></i></a>, <a class="ref" href="analoaf.html#D1" title="ANALOAF:def.1">ANALOAF:def 1</a></i>;<br/><font color="Maroon" title="c17">a</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">t2</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <font color="Maroon" title="c9">t1</font></span>)</span> = 
<font color="Maroon" title="c17">a</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">*</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <span class="p2">(<span class="default"><a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c10">t2</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <font color="Maroon" title="c9">t1</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#T30" title="RLVECT_1:th.30">RLVECT_1:30</a></i>
<br/>.= 
 <a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c18">b</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">*</a> <span class="p2">(<span class="default"><a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c12">w2</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <font color="Maroon" title="c11">w1</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="geomtrap.html#E5:41"><i><font color="Green" title="E43">A5</font></i></a>, <a class="txt" href="geomtrap.html#E3:41_3_1"><i><font color="Green" title="E47">A9</font></i></a>, <a class="ref" href="rlvect_1.html#T39" title="RLVECT_1:th.39">RLVECT_1:39</a></i>
<br/>.= 
<font color="Maroon" title="c18">b</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">*</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <span class="p2">(<span class="default"><a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c12">w2</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <font color="Maroon" title="c11">w1</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#T39" title="RLVECT_1:th.39">RLVECT_1:39</a></i>
<br/>.= 
<font color="Maroon" title="c18">b</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">w2</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <font color="Maroon" title="c11">w1</font></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#T30" title="RLVECT_1:th.30">RLVECT_1:30</a></i>
;<br/><b>hence </b><a NAME="E5:41_3_1"/>
<font color="Maroon" title="c9">t1</font>,<font color="Maroon" title="c10">t2</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c11">w1</font>,<font color="Maroon" title="c12">w2</font>
 <b>by </b><i><a class="txt" href="geomtrap.html#E3:41_3_1"><i><font color="Green" title="E47">A9</font></i></a>, <a class="ref" href="analoaf.html#D1" title="ANALOAF:def.1">ANALOAF:def 1</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:41_3"/>
<font color="Maroon" title="c9">t1</font>,<font color="Maroon" title="c10">t2</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c11">w1</font>,<font color="Maroon" title="c12">w2</font>
 <b>by </b><i><a class="txt" href="geomtrap.html#E6:41"><i><font color="Green" title="E44">A6</font></i></a>, <a class="txt" href="geomtrap.html#E7:41"><i><font color="Green" title="E45">A7</font></i></a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E9:41"/>
( <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">u1</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c6">u2</font></span>)</span> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">t1</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c10">t2</font></span>)</span> &amp; <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="c7">v1</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c8">v2</font></span>)</span> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">w1</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c12">w2</font></span>)</span> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="41_4"><b>proof </b></a><div class="add">

<b>thus </b><span class="p1">(<span class="default"><font color="Maroon" title="c5">u1</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c6">u2</font></span>)</span> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">t1</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c10">t2</font></span>)</span> = 
<font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c4">u</font>
<b>by </b><i><a class="txt" href="geomtrap.html#E2:41"><i><font color="Green" title="E40">A2</font></i></a>, <a class="ref" href="geomtrap.html#T8" target="_self" title="GEOMTRAP:th.8">Th8</a></i>
<br/>.= 
<font color="Maroon" title="c4">u</font>

;<br/>

<b>thus </b><span class="p1">(<span class="default"><font color="Maroon" title="c7">v1</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c8">v2</font></span>)</span> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">w1</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c12">w2</font></span>)</span> = 
<font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c4">u</font>
<b>by </b><i><a class="txt" href="geomtrap.html#E2:41"><i><font color="Green" title="E40">A2</font></i></a>, <a class="ref" href="geomtrap.html#T8" target="_self" title="GEOMTRAP:th.8">Th8</a></i>
<br/>.= 
<font color="Maroon" title="c4">u</font>

;<br/>


</div><b>end;</b></div>
<b>then </b><i><font color="Green" title="E47">A10</font></i>: <span class="p1">(<span class="default"><font color="Maroon" title="c11">w1</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c12">w2</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="c9">t1</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c10">t2</font></span>)</span> = 
 <a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">v1</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c8">v2</font></span>)</span> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">u1</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c6">u2</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="geomtrap.html#E21"><i><font color="Green" title="E18">Lm3</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</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"><font color="Maroon" title="c7">v1</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c8">v2</font></span>)</span> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">u1</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c6">u2</font></span>)</span></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/>
<a NAME="E11:41"/>
( <font color="Maroon" title="c10">t2</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <font color="Maroon" title="c9">t1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">u2</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <font color="Maroon" title="c5">u1</font></span>)</span> &amp; <font color="Maroon" title="c12">w2</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <font color="Maroon" title="c11">w1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <font color="Maroon" title="c7">v1</font></span>)</span> )
 
<b>by </b><i><a class="txt" href="geomtrap.html#E2:41"><i><font color="Green" title="E40">A2</font></i></a>, <a class="txt" href="geomtrap.html#E21"><i><font color="Green" title="E18">Lm3</font></i></a></i>;<br/>
<a NAME="E12:41"/><b>then </b><i><font color="Green" title="E48">A11</font></i>: 
( <font color="Maroon" title="c10">t2</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <font color="Maroon" title="c9">t1</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> 1</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">u2</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <font color="Maroon" title="c5">u1</font></span>)</span> &amp; <font color="Maroon" title="c12">w2</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <font color="Maroon" title="c11">w1</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> 1</span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <font color="Maroon" title="c7">v1</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/>
<a NAME="E13:41"/>
( <font color="Maroon" title="c6">u2</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <font color="Maroon" title="c5">u1</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c7">v1</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c8">v2</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="c5">u1</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c6">u2</font></span>)</span> <a href="analmetr.html#R2" title="ANALMETR:pred.2">are_Ort_wrt</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font> &amp; <font color="Maroon" title="c8">v2</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <font color="Maroon" title="c7">v1</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c7">v1</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c8">v2</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="c5">u1</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c6">u2</font></span>)</span> <a href="analmetr.html#R2" title="ANALMETR:pred.2">are_Ort_wrt</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font> )
 
<b>by </b><i><a class="txt" href="geomtrap.html#E4:41"><i><font color="Green" title="E42">A4</font></i></a>, <a class="ref" href="analmetr.html#D3" title="ANALMETR:def.3">ANALMETR:def 3</a></i>;<br/>
<a NAME="E14:41"/><b>then </b>
( <font color="Maroon" title="c10">t2</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <font color="Maroon" title="c9">t1</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c11">w1</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c12">w2</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="c9">t1</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c10">t2</font></span>)</span> <a href="analmetr.html#R2" title="ANALMETR:pred.2">are_Ort_wrt</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font> &amp; <font color="Maroon" title="c12">w2</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <font color="Maroon" title="c11">w1</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c11">w1</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c12">w2</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="c9">t1</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c10">t2</font></span>)</span> <a href="analmetr.html#R2" title="ANALMETR:pred.2">are_Ort_wrt</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font> )
 
<b>by </b><i><a class="txt" href="geomtrap.html#E10:41"><i><font color="Green" title="E47">A10</font></i></a>, <a class="txt" href="geomtrap.html#E12:41"><i><font color="Green" title="E48">A11</font></i></a>, <a class="ref" href="analmetr.html#T10" title="ANALMETR:th.10">ANALMETR:10</a></i>;<br/>
<a NAME="E15:41"/><b>then </b>
( <font color="Maroon" title="c9">t1</font>,<font color="Maroon" title="c10">t2</font>,<font color="Maroon" title="c9">t1</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c10">t2</font>,<font color="Maroon" title="c11">w1</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c12">w2</font> <a href="analmetr.html#R3" title="ANALMETR:pred.3">are_Ort_wrt</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font> &amp; <font color="Maroon" title="c11">w1</font>,<font color="Maroon" title="c12">w2</font>,<font color="Maroon" title="c9">t1</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c10">t2</font>,<font color="Maroon" title="c11">w1</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c12">w2</font> <a href="analmetr.html#R3" title="ANALMETR:pred.3">are_Ort_wrt</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font> )
 
<b>by </b><i><a class="ref" href="analmetr.html#D3" title="ANALMETR:def.3">ANALMETR:def 3</a></i>;<br/>
<b>hence </b><a NAME="E16:41"/>
<font color="Maroon" title="c9">t1</font>,<font color="Maroon" title="c10">t2</font>,<font color="Maroon" title="c11">w1</font>,<font color="Maroon" title="c12">w2</font> <a href="geomtrap.html#R2" title="GEOMTRAP:pred.2">are_DTr_wrt</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>
 <b>by </b><i><a class="txt" href="geomtrap.html#E8:41"><i><font color="Green" title="E46">A8</font></i></a>, <a class="ref" href="geomtrap.html#D3" target="_self" title="GEOMTRAP:def.3">Def3</a></i>;<br/>


</div>
