<?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">u'</font>, <font color="Olive" title="b5">u1</font>, <font color="Olive" title="b6">u2</font>, <font color="Olive" title="b7">v1</font>, <font color="Olive" title="b8">v2</font>, <font color="Olive" title="b9">t1</font>, <font color="Olive" title="b10">t2</font>, <font color="Olive" title="b11">w1</font>, <font color="Olive" title="b12">w2</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> &amp; <font color="Olive" title="b3">u</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b4">u'</font> &amp; <font color="Olive" title="b3">u</font>,<font color="Olive" title="b4">u'</font>,<font color="Olive" title="b5">u1</font>,<font color="Olive" title="b9">t1</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> &amp; <font color="Olive" title="b3">u</font>,<font color="Olive" title="b4">u'</font>,<font color="Olive" title="b6">u2</font>,<font color="Olive" title="b10">t2</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> &amp; <font color="Olive" title="b3">u</font>,<font color="Olive" title="b4">u'</font>,<font color="Olive" title="b7">v1</font>,<font color="Olive" title="b11">w1</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> &amp; <font color="Olive" title="b3">u</font>,<font color="Olive" title="b4">u'</font>,<font color="Olive" title="b8">v2</font>,<font color="Olive" title="b12">w2</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> &amp; <font color="Olive" title="b5">u1</font>,<font color="Olive" title="b6">u2</font>,<font color="Olive" title="b7">v1</font>,<font color="Olive" title="b8">v2</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> holds <br/><font color="Olive" title="b9">t1</font>,<font color="Olive" title="b10">t2</font>,<font color="Olive" title="b11">w1</font>,<font color="Olive" title="b12">w2</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> 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"> for <font color="Olive" title="b1">u</font>, <font color="Olive" title="b2">u'</font>, <font color="Olive" title="b3">u1</font>, <font color="Olive" title="b4">u2</font>, <font color="Olive" title="b5">v1</font>, <font color="Olive" title="b6">v2</font>, <font color="Olive" title="b7">t1</font>, <font color="Olive" title="b8">t2</font>, <font color="Olive" title="b9">w1</font>, <font color="Olive" title="b10">w2</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="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font> &amp; <font color="Olive" title="b1">u</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">u'</font> &amp; <font color="Olive" title="b1">u</font>,<font color="Olive" title="b2">u'</font>,<font color="Olive" title="b3">u1</font>,<font color="Olive" title="b7">t1</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> &amp; <font color="Olive" title="b1">u</font>,<font color="Olive" title="b2">u'</font>,<font color="Olive" title="b4">u2</font>,<font color="Olive" title="b8">t2</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> &amp; <font color="Olive" title="b1">u</font>,<font color="Olive" title="b2">u'</font>,<font color="Olive" title="b5">v1</font>,<font color="Olive" title="b9">w1</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> &amp; <font color="Olive" title="b1">u</font>,<font color="Olive" title="b2">u'</font>,<font color="Olive" title="b6">v2</font>,<font color="Olive" title="b10">w2</font> <a href="geomtrap.html#R2" title="GEOMTRAP:pred.2">are_DTr_wrt</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font> &amp; <font color="Olive" title="b3">u1</font>,<font color="Olive" title="b4">u2</font>,<font color="Olive" title="b5">v1</font>,<font color="Olive" title="b6">v2</font> <a href="geomtrap.html#R2" title="GEOMTRAP:pred.2">are_DTr_wrt</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font> holds <br/><font color="Olive" title="b7">t1</font>,<font color="Olive" title="b8">t2</font>,<font color="Olive" title="b9">w1</font>,<font color="Olive" title="b10">w2</font> <a href="geomtrap.html#R2" title="GEOMTRAP:pred.2">are_DTr_wrt</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font></span><br/><b>let </b><font color="Maroon" title="c4">u</font>, <font color="Maroon" title="c5">u'</font>, <font color="Maroon" title="c6">u1</font>, <font color="Maroon" title="c7">u2</font>, <font color="Maroon" title="c8">v1</font>, <font color="Maroon" title="c9">v2</font>, <font color="Maroon" title="c10">t1</font>, <font color="Maroon" title="c11">t2</font>, <font color="Maroon" title="c12">w1</font>, <font color="Maroon" title="c13">w2</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> &amp; <font color="Maroon" title="c4">u</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">u'</font> &amp; <font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">u'</font>,<font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c10">t1</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> &amp; <font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">u'</font>,<font color="Maroon" title="c7">u2</font>,<font color="Maroon" title="c11">t2</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> &amp; <font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">u'</font>,<font color="Maroon" title="c8">v1</font>,<font color="Maroon" title="c12">w1</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> &amp; <font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">u'</font>,<font color="Maroon" title="c9">v2</font>,<font color="Maroon" title="c13">w2</font> <a href="geomtrap.html#R2" title="GEOMTRAP:pred.2">are_DTr_wrt</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font> &amp; <font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c7">u2</font>,<font color="Maroon" title="c8">v1</font>,<font color="Maroon" title="c9">v2</font> <a href="geomtrap.html#R2" title="GEOMTRAP:pred.2">are_DTr_wrt</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font> implies <font color="Maroon" title="c10">t1</font>,<font color="Maroon" title="c11">t2</font>,<font color="Maroon" title="c12">w1</font>,<font color="Maroon" title="c13">w2</font> <a href="geomtrap.html#R2" title="GEOMTRAP:pred.2">are_DTr_wrt</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font> )</span><br/>







<b>assume </b><b>that </b><br/><a NAME="E1:67"/><i><font color="Green" title="E63">A1</font></i>: 
 <a href="analmetr.html#R1" title="ANALMETR:pred.1">Gen</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>
 <b>and </b><br/><a NAME="E2:67"/><i><font color="Green" title="E64">A2</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">u'</font>
 <b>and </b><br/><a NAME="E3:67"/><i><font color="Green" title="E65">A3</font></i>: 
( <font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">u'</font>,<font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c10">t1</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> &amp; <font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">u'</font>,<font color="Maroon" title="c7">u2</font>,<font color="Maroon" title="c11">t2</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> &amp; <font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">u'</font>,<font color="Maroon" title="c8">v1</font>,<font color="Maroon" title="c12">w1</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> &amp; <font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">u'</font>,<font color="Maroon" title="c9">v2</font>,<font color="Maroon" title="c13">w2</font> <a href="geomtrap.html#R2" title="GEOMTRAP:pred.2">are_DTr_wrt</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font> )
 <b>and </b><br/><a NAME="E4:67"/><i><font color="Green" title="E66">A4</font></i>: 
<font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c7">u2</font>,<font color="Maroon" title="c8">v1</font>,<font color="Maroon" title="c9">v2</font> <a href="geomtrap.html#R2" title="GEOMTRAP:pred.2">are_DTr_wrt</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c10">t1</font>,<font color="Maroon" title="c11">t2</font>,<font color="Maroon" title="c12">w1</font>,<font color="Maroon" title="c13">w2</font> <a href="geomtrap.html#R2" title="GEOMTRAP:pred.2">are_DTr_wrt</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font></span><br/>

<a NAME="E5:67"/><i><font color="Green" title="E67">A5</font></i>: 
<font color="Maroon" title="c10">t1</font>,<font color="Maroon" title="c11">t2</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c12">w1</font>,<font color="Maroon" title="c13">w2</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="67_1"><b>proof </b></a><div class="add">

<a NAME="E1:67_1"/>
<font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c7">u2</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c8">v1</font>,<font color="Maroon" title="c9">v2</font>
 
<b>by </b><i><a class="txt" href="#E4:67"><i><font color="Green" title="E66">A4</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="E2:67_1"/>
<font color="Maroon" title="c10">t1</font>,<font color="Maroon" title="c11">t2</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c12">w1</font>,<font color="Maroon" title="c13">w2</font>
 <b>by </b><i><a class="txt" href="#E1:67"><i><font color="Green" title="E63">A1</font></i></a>, <a class="txt" href="#E2:67"><i><font color="Green" title="E64">A2</font></i></a>, <a class="txt" href="#E3:67"><i><font color="Green" title="E65">A3</font></i></a>, <a class="ref" href="geomtrap.html#T39" target="_self" title="GEOMTRAP:th.39">Th39</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>set </b><font color="Maroon" title="c14">uu</font> = <font color="Maroon" title="c6">u1</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c7">u2</font>;<br/>
<b>set </b><font color="Maroon" title="c15">vv</font> = <font color="Maroon" title="c8">v1</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c9">v2</font>;<br/>
<a NAME="E6:67"/><i><font color="Green" title="E68">A6</font></i>: 
( <font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">u'</font>,<font color="Maroon" title="c6">u1</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c7">u2</font>,<font color="Maroon" title="c10">t1</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c11">t2</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> &amp; <font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">u'</font>,<font color="Maroon" title="c8">v1</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c9">v2</font>,<font color="Maroon" title="c12">w1</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c13">w2</font> <a href="geomtrap.html#R2" title="GEOMTRAP:pred.2">are_DTr_wrt</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font> )
 
<b>by </b><i><a class="txt" href="#E1:67"><i><font color="Green" title="E63">A1</font></i></a>, <a class="txt" href="#E2:67"><i><font color="Green" title="E64">A2</font></i></a>, <a class="txt" href="#E3:67"><i><font color="Green" title="E65">A3</font></i></a>, <a class="ref" href="geomtrap.html#T41" target="_self" title="GEOMTRAP:th.41">Th41</a></i>;<br/>
<a NAME="E7:67"/>
<font color="Maroon" title="c6">u1</font>,<font color="Maroon" title="c7">u2</font>,<font color="Maroon" title="c6">u1</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c7">u2</font>,<font color="Maroon" title="c8">v1</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c9">v2</font> <a href="analmetr.html#R3" title="ANALMETR:pred.3">are_Ort_wrt</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>
 
<b>by </b><i><a class="txt" href="#E4:67"><i><font color="Green" title="E66">A4</font></i></a>, <a class="ref" href="geomtrap.html#D3" target="_self" title="GEOMTRAP:def.3">Def3</a></i>;<br/>
<a NAME="E8:67"/><b>then </b><i><font color="Green" title="E69">A7</font></i>: 
<font color="Maroon" title="c10">t1</font>,<font color="Maroon" title="c11">t2</font>,<font color="Maroon" title="c10">t1</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c11">t2</font>,<font color="Maroon" title="c12">w1</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c13">w2</font> <a href="analmetr.html#R3" title="ANALMETR:pred.3">are_Ort_wrt</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>
 
<b>by </b><i><a class="txt" href="#E1:67"><i><font color="Green" title="E63">A1</font></i></a>, <a class="txt" href="#E2:67"><i><font color="Green" title="E64">A2</font></i></a>, <a class="txt" href="#E3:67"><i><font color="Green" title="E65">A3</font></i></a>, <a class="txt" href="#E6:67"><i><font color="Green" title="E68">A6</font></i></a>, <a class="ref" href="geomtrap.html#T42" target="_self" title="GEOMTRAP:th.42">Th42</a></i>;<br/>
<a NAME="E9:67"/>
<font color="Maroon" title="c8">v1</font>,<font color="Maroon" title="c9">v2</font>,<font color="Maroon" title="c6">u1</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c7">u2</font>,<font color="Maroon" title="c8">v1</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c9">v2</font> <a href="analmetr.html#R3" title="ANALMETR:pred.3">are_Ort_wrt</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>
 
<b>by </b><i><a class="txt" href="#E4:67"><i><font color="Green" title="E66">A4</font></i></a>, <a class="ref" href="geomtrap.html#D3" target="_self" title="GEOMTRAP:def.3">Def3</a></i>;<br/>
<a NAME="E10:67"/><b>then </b>
<font color="Maroon" title="c12">w1</font>,<font color="Maroon" title="c13">w2</font>,<font color="Maroon" title="c10">t1</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c11">t2</font>,<font color="Maroon" title="c12">w1</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c13">w2</font> <a href="analmetr.html#R3" title="ANALMETR:pred.3">are_Ort_wrt</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>
 
<b>by </b><i><a class="txt" href="#E1:67"><i><font color="Green" title="E63">A1</font></i></a>, <a class="txt" href="#E2:67"><i><font color="Green" title="E64">A2</font></i></a>, <a class="txt" href="#E3:67"><i><font color="Green" title="E65">A3</font></i></a>, <a class="txt" href="#E6:67"><i><font color="Green" title="E68">A6</font></i></a>, <a class="ref" href="geomtrap.html#T42" target="_self" title="GEOMTRAP:th.42">Th42</a></i>;<br/>
<b>hence </b><a NAME="E11:67"/>
<font color="Maroon" title="c10">t1</font>,<font color="Maroon" title="c11">t2</font>,<font color="Maroon" title="c12">w1</font>,<font color="Maroon" title="c13">w2</font> <a href="geomtrap.html#R2" title="GEOMTRAP:pred.2">are_DTr_wrt</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>
 <b>by </b><i><a class="txt" href="#E5:67"><i><font color="Green" title="E67">A5</font></i></a>, <a class="txt" href="#E8:67"><i><font color="Green" title="E69">A7</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/>


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