<?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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">w</font>, <font color="Olive" title="b2">y</font>, <font color="Olive" title="b3">u</font>, <font color="Olive" title="b4">v</font>, <font color="Olive" title="b5">u1</font> being  <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font>  st  <a href="analmetr.html#R1" title="ANALMETR:pred.1">Gen</a> <font color="Olive" title="b1">w</font>,<font color="Olive" title="b2">y</font> holds <br/> ex <font color="Olive" title="b6">t</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="Olive" title="b3">u</font>,<font color="Olive" title="b4">v</font>,<font color="Olive" title="b5">u1</font>,<font color="Olive" title="b6">t</font> <a href="geomtrap.html#R2" title="GEOMTRAP:pred.2">are_DTr_wrt</a> <font color="Olive" title="b1">w</font>,<font color="Olive" title="b2">y</font> or <font color="Olive" title="b3">u</font>,<font color="Olive" title="b4">v</font>,<font color="Olive" title="b6">t</font>,<font color="Olive" title="b5">u1</font> <a href="geomtrap.html#R2" title="GEOMTRAP:pred.2">are_DTr_wrt</a> <font color="Olive" title="b1">w</font>,<font color="Olive" title="b2">y</font> )</span><br/><b>let </b><font color="Maroon" title="c2">w</font>, <font color="Maroon" title="c3">y</font>, <font color="Maroon" title="c4">u</font>, <font color="Maroon" title="c5">v</font>, <font color="Maroon" title="c6">u1</font> be   <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <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> implies  ex <font color="Olive" title="b1">t</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="c4">u</font>,<font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c6">u1</font>,<font color="Olive" title="b1">t</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> or <font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font>,<font color="Olive" title="b1">t</font>,<font color="Maroon" title="c6">u1</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> ) )</span><br/>











<b>assume </b><a NAME="E1:33"/><i><font color="Green" title="E31">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>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">t</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="c4">u</font>,<font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c6">u1</font>,<font color="Olive" title="b1">t</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> or <font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font>,<font color="Olive" title="b1">t</font>,<font color="Maroon" title="c6">u1</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> )</span><br/>

<b>set </b><font color="Maroon" title="c7">a</font> = <font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font>;<br/>
<div><i><font color="Green" title="E32">A2</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="33_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:33_1"/><i><font color="Green" title="E33">A3</font></i>: 
<font color="Maroon" title="c4">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">v</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">t</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="c4">u</font>,<font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c6">u1</font>,<font color="Olive" title="b1">t</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> or <font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font>,<font color="Olive" title="b1">t</font>,<font color="Maroon" title="c6">u1</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> )</span><br/><a NAME="E2:33_1"/>
( <font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c4">u</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c6">u1</font> &amp; <font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c6">u1</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c4">u</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="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c6">u1</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c6">u1</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#E1:33"><i><font color="Green" title="E31">A1</font></i></a>, <a class="txt" href="geomtrap.html#E24"><i><font color="Green" title="E21">Lm5</font></i></a>, <a class="ref" href="analoaf.html#T18" title="ANALOAF:th.18">ANALOAF:18</a></i>;<br/><a NAME="E3:33_1"/><b>then </b>
( <font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c4">u</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c6">u1</font> &amp; <font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c6">u1</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c6">u1</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="c6">u1</font>,<font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c6">u1</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c6">u1</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#E1:33"><i><font color="Green" title="E31">A1</font></i></a>, <a class="txt" href="geomtrap.html#E23"><i><font color="Green" title="E20">Lm4A</font></i></a></i>;<br/><a NAME="E4:33_1"/><b>then </b>
<font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c6">u1</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="ref" href="geomtrap.html#D3" target="_self" title="GEOMTRAP:def.3">Def3</a></i>;<br/><b>hence </b><a NAME="E5:33_1"/>
 ex <font color="Olive" title="b1">t</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="c4">u</font>,<font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c6">u1</font>,<font color="Olive" title="b1">t</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> or <font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font>,<font color="Olive" title="b1">t</font>,<font color="Maroon" title="c6">u1</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#E1:33_1"><i><font color="Green" title="E33">A3</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="33_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:33_2"/><i><font color="Green" title="E33">A4</font></i>: 
<font color="Maroon" title="c4">u</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">v</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">t</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="c4">u</font>,<font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c6">u1</font>,<font color="Olive" title="b1">t</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> or <font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font>,<font color="Olive" title="b1">t</font>,<font color="Maroon" title="c6">u1</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> )</span><br/><a NAME="E2:33_2"/>
<font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">u</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="33_2_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:33_2_1"/>
<font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">u</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:33_2_1"/><b>then </b>
<font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c4">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font>
 
;<br/>
<b>hence </b><a NAME="E3:33_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="geomtrap.html#E1:33_2"><i><font color="Green" title="E33">A4</font></i></a>, <a class="ref" href="geomtrap.html#T9" target="_self" title="GEOMTRAP:th.9">Th9</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E3:33_2"/><b>then </b>
<font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font></span>)</span> <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="ref" href="rlvect_1.html#T35" title="RLVECT_1:th.35">RLVECT_1:35</a></i>;<br/><b>then consider </b><font color="Maroon" title="c8">r</font> being   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a><b> such that </b><br/><a NAME="E5:33_2"/><i><font color="Green" title="E34">A5</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">u1</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">r</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</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#E1:33"><i><font color="Green" title="E31">A1</font></i></a>, <a class="ref" href="analmetr.html#T17" title="ANALMETR:th.17">ANALMETR:17</a></i>;<br/><b>set </b><font color="Maroon" title="c9">b</font> = <font color="Maroon" title="c6">u1</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">r</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font></span>)</span></span>)</span></span>)</span>;<br/><b>set </b><font color="Maroon" title="c10">t</font> = <span class="p1">(<span class="default">2 <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">u1</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c8">r</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c6">u1</font>;<br/><a NAME="E6:33_2"/><i><font color="Green" title="E35">A6</font></i>: 
<font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="geomtrap.html#T12" target="_self" title="GEOMTRAP:th.12">Th12</a></i>;<br/><a NAME="E7:33_2"/><i><font color="Green" title="E36">A7</font></i>: 
<font color="Maroon" title="c6">u1</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">u1</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c8">r</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c6">u1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">u1</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">r</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font></span>)</span></span>)</span></span>)</span>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="33_2_2"><b>proof </b></a><div class="add">

<font color="Maroon" title="c6">u1</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">2 <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">u1</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c8">r</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c6">u1</font></span>)</span> = 
<span class="p1">(<span class="default">1 <a href="real_1.html#K7" title="REAL_1:func.7">+</a> 1</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">u1</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">r</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font></span>)</span></span>)</span></span>)</span></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">1 <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">u1</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c8">r</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default">1 <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">u1</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c8">r</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font></span>)</span></span>)</span></span>)</span></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/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">u1</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">r</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default">1 <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">u1</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c8">r</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font></span>)</span></span>)</span></span>)</span></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/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">u1</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">r</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font></span>)</span></span>)</span></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="c6">u1</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">r</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font></span>)</span></span>)</span></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/>
<b>hence </b><a NAME="E2:33_2_2"/>
<font color="Maroon" title="c6">u1</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">u1</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c8">r</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c6">u1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">u1</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">r</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="geomtrap.html#D2" target="_self" title="GEOMTRAP:def.2">Def2</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E8:33_2"/><i><font color="Green" title="E37">A8</font></i>: 
<font color="Maroon" title="c6">u1</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">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="c8">r</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">u1</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">r</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font></span>)</span>
 <b>by </b><i><a class="ref" href="rlvect_1.html#T41" title="RLVECT_1:th.41">RLVECT_1:41</a></i>;<br/><a NAME="E9:33_2"/><b>then </b><i><font color="Green" title="E38">A9</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">u1</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">r</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">u1</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">r</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="rlvect_1.html#T41" title="RLVECT_1:th.41">RLVECT_1:41</a></i>;<br/><a NAME="E10:33_2"/><i><font color="Green" title="E39">A10</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">u1</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">r</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font></span>)</span>,<font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</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#E5:33_2"><i><font color="Green" title="E34">A5</font></i></a>, <a class="txt" href="geomtrap.html#E8:33_2"><i><font color="Green" title="E37">A8</font></i></a>, <a class="ref" href="rlvect_1.html#T41" title="RLVECT_1:th.41">RLVECT_1:41</a></i>;<br/><a NAME="E11:33_2"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c6">u1</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">r</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font></span>)</span>,<font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c5">v</font> <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#E5:33_2"><i><font color="Green" title="E34">A5</font></i></a>, <a class="txt" href="geomtrap.html#E6:33_2"><i><font color="Green" title="E35">A6</font></i></a>, <a class="txt" href="geomtrap.html#E9:33_2"><i><font color="Green" title="E38">A9</font></i></a>, <a class="ref" href="analmetr.html#T11" title="ANALMETR:th.11">ANALMETR:11</a></i>;<br/><a NAME="E12:33_2"/><b>then </b>
<font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c6">u1</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">r</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c4">u</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/><a NAME="E13:33_2"/><b>then </b>
<font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c6">u1</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">r</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</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#E1:33"><i><font color="Green" title="E31">A1</font></i></a>, <a class="txt" href="geomtrap.html#E22"><i><font color="Green" title="E19">Lm4</font></i></a></i>;<br/><a NAME="E14:33_2"/><b>then </b><i><font color="Green" title="E40">A11</font></i>: 
<font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c6">u1</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">u1</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c8">r</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c6">u1</font></span>)</span> <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#E1:33"><i><font color="Green" title="E31">A1</font></i></a>, <a class="txt" href="geomtrap.html#E7:33_2"><i><font color="Green" title="E36">A7</font></i></a>, <a class="txt" href="geomtrap.html#E23"><i><font color="Green" title="E20">Lm4A</font></i></a></i>;<br/><font color="Maroon" title="c6">u1</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">u1</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">r</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font></span>)</span></span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">u1</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c6">u1</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="c8">r</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#T43" title="RLVECT_1:th.43">RLVECT_1:43</a></i>
<br/>.= 
<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="c8">r</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#T28" title="RLVECT_1:th.28">RLVECT_1:28</a></i>
<br/>.= 
<font color="Maroon" title="c8">r</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font></span>)</span></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/><b>then </b><i><font color="Green" title="E41">A12</font></i>: <font color="Maroon" title="c6">u1</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">u1</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c8">r</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c6">u1</font></span>)</span> = 
2 <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">r</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="geomtrap.html#E7:33_2"><i><font color="Green" title="E36">A7</font></i></a>, <a class="ref" href="geomtrap.html#T12" target="_self" title="GEOMTRAP:th.12">Th12</a></i>
<br/>.= 
<span class="p1">(<span class="default">2 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c8">r</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">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</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/><a NAME="E17:33_2"/><b>then </b><i><font color="Green" title="E42">A13</font></i>: 
<font color="Maroon" title="c6">u1</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">u1</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c8">r</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c6">u1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">r</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c5">v</font></span>)</span>
 <b>by </b><i><a class="txt" href="geomtrap.html#E6:33_2"><i><font color="Green" title="E35">A6</font></i></a>, <a class="ref" href="rlvect_1.html#D9" title="RLVECT_1:def.9">RLVECT_1:def 9</a></i>;<br/><div><i><font color="Green" title="E43">A14</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="33_2_5"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:33_2_5"/><i><font color="Green" title="E44">A15</font></i>: 
<font color="Maroon" title="c8">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">t</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="c4">u</font>,<font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c6">u1</font>,<font color="Olive" title="b1">t</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> or <font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font>,<font color="Olive" title="b1">t</font>,<font color="Maroon" title="c6">u1</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> )</span><br/><a NAME="E2:33_2_5"/><i><font color="Green" title="E45">A16</font></i>: 
( <font color="Maroon" title="c6">u1</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">r</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">u1</font> &amp; <span class="p1">(<span class="default">2 <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">u1</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c8">r</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c6">u1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">u1</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="33_2_5_1"><b>proof </b></a><div class="add">

<b>thus </b><font color="Maroon" title="c6">u1</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">r</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font></span>)</span></span>)</span></span>)</span> = 
<font color="Maroon" title="c6">u1</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</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="geomtrap.html#E1:33_2_5"><i><font color="Green" title="E44">A15</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">u1</font>
<b>by </b><i><a class="ref" href="rlvect_1.html#T26" title="RLVECT_1:th.26">RLVECT_1:26</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default">2 <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">u1</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c8">r</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c6">u1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">u1</font></span><br/>

<b>hence </b><span class="p1">(<span class="default">2 <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">u1</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c8">r</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c6">u1</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K7" title="REAL_1:func.7">+</a> 1</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c6">u1</font></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c6">u1</font>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c6">u1</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default">1 <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c6">u1</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c6">u1</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"><font color="Maroon" title="c6">u1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default">1 <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c6">u1</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c6">u1</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"><font color="Maroon" title="c6">u1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c6">u1</font></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c6">u1</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/>.= 
<font color="Maroon" title="c6">u1</font>
<b>by </b><i><a class="ref" href="rlsub_2.html#T78" title="RLSUB_2:th.78">RLSUB_2:78</a></i>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E3:33_2_5"/>
( <font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c6">u1</font>,<span class="p1">(<span class="default">2 <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">u1</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c8">r</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c6">u1</font> &amp; <font color="Maroon" title="c6">u1</font>,<span class="p1">(<span class="default">2 <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">u1</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c8">r</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c6">u1</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">u1</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c8">r</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c6">u1</font></span>)</span> <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> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="33_2_5_2"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:33_2_5_2"/>
<font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c6">u1</font>,<span class="p1">(<span class="default">2 <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">u1</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c8">r</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c6">u1</font>
 <b>by </b><i><a class="txt" href="geomtrap.html#E2:33_2_5"><i><font color="Green" title="E45">A16</font></i></a>, <a class="ref" href="analoaf.html#T18" title="ANALOAF:th.18">ANALOAF:18</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c6">u1</font>,<span class="p1">(<span class="default">2 <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">u1</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c8">r</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c6">u1</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">u1</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c8">r</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c6">u1</font></span>)</span> <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></span><br/>

<a NAME="E2:33_2_5_2"/>
<font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c6">u1</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">r</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c6">u1</font>,<span class="p1">(<span class="default">2 <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">u1</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c8">r</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c6">u1</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#E1:33"><i><font color="Green" title="E31">A1</font></i></a>, <a class="txt" href="geomtrap.html#E2:33_2_5"><i><font color="Green" title="E45">A16</font></i></a>, <a class="txt" href="geomtrap.html#E24"><i><font color="Green" title="E21">Lm5</font></i></a></i>;<br/>
<b>hence </b><a NAME="E3:33_2_5_2"/>
<font color="Maroon" title="c6">u1</font>,<span class="p1">(<span class="default">2 <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">u1</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c8">r</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c6">u1</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">u1</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c8">r</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c6">u1</font></span>)</span> <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#E1:33"><i><font color="Green" title="E31">A1</font></i></a>, <a class="txt" href="geomtrap.html#E7:33_2"><i><font color="Green" title="E36">A7</font></i></a>, <a class="txt" href="geomtrap.html#E23"><i><font color="Green" title="E20">Lm4A</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E4:33_2_5"/><b>then </b>
<font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c6">u1</font>,<span class="p1">(<span class="default">2 <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">u1</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c8">r</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c6">u1</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#E14:33_2"><i><font color="Green" title="E40">A11</font></i></a>, <a class="ref" href="geomtrap.html#D3" target="_self" title="GEOMTRAP:def.3">Def3</a></i>;<br/><b>hence </b><a NAME="E5:33_2_5"/>
 ex <font color="Olive" title="b1">t</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="c4">u</font>,<font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c6">u1</font>,<font color="Olive" title="b1">t</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> or <font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font>,<font color="Olive" title="b1">t</font>,<font color="Maroon" title="c6">u1</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> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="33_2_6"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:33_2_6"/>
<font color="Maroon" title="c8">r</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c6">u1</font>,<span class="p1">(<span class="default">2 <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">u1</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c8">r</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c6">u1</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> or <font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font>,<span class="p1">(<span class="default">2 <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">u1</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c8">r</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c6">u1</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> )</span><br/><a NAME="E2:33_2_6"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c6">u1</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">r</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font></span>)</span>,<font color="Maroon" title="c6">u1</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">u1</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c8">r</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c6">u1</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#E10:33_2"><i><font color="Green" title="E39">A10</font></i></a>, <a class="txt" href="geomtrap.html#E16:33_2"><i><font color="Green" title="E41">A12</font></i></a>, <a class="ref" href="analmetr.html#T11" title="ANALMETR:th.11">ANALMETR:11</a></i>;<br/><a NAME="E3:33_2_6"/><b>then </b><i><font color="Green" title="E44">A17</font></i>: 
<font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c6">u1</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">r</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default">2 <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">u1</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c8">r</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c6">u1</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/><a NAME="E4:33_2_6"/><b>then </b>
<font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c6">u1</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">r</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c6">u1</font>,<span class="p1">(<span class="default">2 <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">u1</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c8">r</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c6">u1</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#E1:33"><i><font color="Green" title="E31">A1</font></i></a>, <a class="txt" href="geomtrap.html#E22"><i><font color="Green" title="E19">Lm4</font></i></a></i>;<br/><a NAME="E5:33_2_6"/><b>then </b><i><font color="Green" title="E45">A18</font></i>: 
<font color="Maroon" title="c6">u1</font>,<span class="p1">(<span class="default">2 <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">u1</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c8">r</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c6">u1</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">u1</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c8">r</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c6">u1</font></span>)</span> <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#E1:33"><i><font color="Green" title="E31">A1</font></i></a>, <a class="txt" href="geomtrap.html#E7:33_2"><i><font color="Green" title="E36">A7</font></i></a>, <a class="txt" href="geomtrap.html#E23"><i><font color="Green" title="E20">Lm4A</font></i></a></i>;<br/><a NAME="E6:33_2_6"/><i><font color="Green" title="E46">A19</font></i>: 
<span class="p1">(<span class="default">2 <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">u1</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c8">r</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">u1</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c8">r</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c6">u1</font></span>)</span> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c6">u1</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#E1:33"><i><font color="Green" title="E31">A1</font></i></a>, <a class="txt" href="geomtrap.html#E7:33_2"><i><font color="Green" title="E36">A7</font></i></a>, <a class="txt" href="geomtrap.html#E3:33_2_6"><i><font color="Green" title="E44">A17</font></i></a>, <a class="txt" href="geomtrap.html#E23"><i><font color="Green" title="E20">Lm4A</font></i></a></i>;<br/><a NAME="E7:33_2_6"/>
<font color="Maroon" title="c8">r</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c5">v</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">u1</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">u1</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c8">r</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p0">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c6">u1</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="geomtrap.html#E17:33_2"><i><font color="Green" title="E42">A13</font></i></a>, <a class="ref" href="rlvect_1.html#D9" title="RLVECT_1:def.9">RLVECT_1:def 9</a></i>;<br/><a NAME="E8:33_2_6"/><b>then </b>
( <font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c4">u</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <span class="p1">(<span class="default">2 <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">u1</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c8">r</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c6">u1</font> or <font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c4">u</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c6">u1</font>,<span class="p1">(<span class="default">2 <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">u1</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c8">r</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c6">u1</font> )
 <b>by </b><i><a class="ref" href="analmetr.html#T18" title="ANALMETR:th.18">ANALMETR:18</a></i>;<br/><a NAME="E9:33_2_6"/><b>then </b>
( <font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c6">u1</font>,<span class="p1">(<span class="default">2 <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">u1</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c8">r</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c6">u1</font> or <font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <span class="p1">(<span class="default">2 <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">u1</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c8">r</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c6">u1</font> )
 <b>by </b><i><a class="ref" href="analoaf.html#T21" title="ANALOAF:th.21">ANALOAF:21</a></i>;<br/><b>hence </b><a NAME="E10:33_2_6"/>
( <font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c6">u1</font>,<span class="p1">(<span class="default">2 <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">u1</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c8">r</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c6">u1</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> or <font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font>,<span class="p1">(<span class="default">2 <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">u1</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c8">r</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c6">u1</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#E14:33_2"><i><font color="Green" title="E40">A11</font></i></a>, <a class="txt" href="geomtrap.html#E5:33_2_6"><i><font color="Green" title="E45">A18</font></i></a>, <a class="txt" href="geomtrap.html#E6:33_2_6"><i><font color="Green" title="E46">A19</font></i></a>, <a class="ref" href="geomtrap.html#D3" target="_self" title="GEOMTRAP:def.3">Def3</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><b>hence </b><a NAME="E20:33_2"/>
 ex <font color="Olive" title="b1">t</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="c4">u</font>,<font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c6">u1</font>,<font color="Olive" title="b1">t</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> or <font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font>,<font color="Olive" title="b1">t</font>,<font color="Maroon" title="c6">u1</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#E18:33_2"><i><font color="Green" title="E43">A14</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:33"/>
 ex <font color="Olive" title="b1">t</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="c4">u</font>,<font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c6">u1</font>,<font color="Olive" title="b1">t</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> or <font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font>,<font color="Olive" title="b1">t</font>,<font color="Maroon" title="c6">u1</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#E2:33"><i><font color="Green" title="E32">A2</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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