<?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">v</font>, <font color="Olive" title="b4">u1</font>, <font color="Olive" title="b5">u2</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">v</font>,<font color="Olive" title="b4">u1</font>,<font color="Olive" title="b3">v</font>,<font color="Olive" title="b5">u2</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="b4">u1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">u2</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">v</font>, <font color="Maroon" title="c5">u1</font>, <font color="Maroon" title="c6">u2</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">v</font>,<font color="Maroon" title="c5">u1</font>,<font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c6">u2</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="c5">u1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">u2</font> )</span><br/>











<b>assume </b><b>that </b><br/><a NAME="E1:37"/><i><font color="Green" title="E35">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="E2:37"/><i><font color="Green" title="E36">A2</font></i>: 
<font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c5">u1</font>,<font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c6">u2</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="c5">u1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">u2</font></span><br/>

<a NAME="E3:37"/><i><font color="Green" title="E37">A3</font></i>: 
( <font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c5">u1</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c6">u2</font> &amp; <font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c5">u1</font>,<font color="Maroon" title="c4">v</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">u1</font>,<font color="Maroon" title="c4">v</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c6">u2</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">v</font>,<font color="Maroon" title="c6">u2</font>,<font color="Maroon" title="c4">v</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">u1</font>,<font color="Maroon" title="c4">v</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c6">u2</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#E2:37"><i><font color="Green" title="E36">A2</font></i></a>, <a class="ref" href="geomtrap.html#D3" target="_self" title="GEOMTRAP:def.3">Def3</a></i>;<br/>
<b>set </b><font color="Maroon" title="c7">b</font> = <font color="Maroon" title="c4">v</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">u1</font>;<br/>
<b>set </b><font color="Maroon" title="c8">c</font> = <font color="Maroon" title="c4">v</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c6">u2</font>;<br/>
<b>assume </b><a NAME="E4:37"/><i><font color="Green" title="E38">A4</font></i>: 
<font color="Maroon" title="c5">u1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">u2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E5:37"/><i><font color="Green" title="E39">A5</font></i>: 
( <font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c5">u1</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c6">u2</font> &amp; <font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c6">u2</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c5">u1</font> )
 
<b>by </b><i><a class="txt" href="geomtrap.html#E3:37"><i><font color="Green" title="E37">A3</font></i></a>, <a class="ref" href="analoaf.html#T21" title="ANALOAF:th.21">ANALOAF:21</a></i>;<br/>
<a NAME="E6:37"/><i><font color="Green" title="E40">A6</font></i>: 
( <font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c5">u1</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c4">v</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">u1</font> &amp; <font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c6">u2</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c4">v</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c6">u2</font> )
 
<b>by </b><i><a class="ref" href="geomtrap.html#T14" target="_self" title="GEOMTRAP:th.14">Th14</a></i>;<br/>
<a NAME="E7:37"/><i><font color="Green" title="E41">A7</font></i>: 
( <font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c5">u1</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c5">u1</font> &amp; <font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c5">u1</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c4">v</font> &amp; <font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c6">u2</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c6">u2</font> &amp; <font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c6">u2</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c4">v</font> )
 
<b>by </b><i><a class="ref" href="analoaf.html#T17" title="ANALOAF:th.17">ANALOAF:17</a>, <a class="ref" href="analoaf.html#T18" title="ANALOAF:th.18">ANALOAF:18</a></i>;<br/>
<a NAME="E8:37"/><i><font color="Green" title="E42">A8</font></i>: 
<font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c5">u1</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c4">v</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c6">u2</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_1"><b>proof </b></a><div class="add">

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:37_1_1"/>
<font color="Maroon" title="c4">v</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">v</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c6">u2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c5">u1</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c4">v</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c6">u2</font></span><br/><a NAME="E2:37_1_1"/><b>then </b>
<font color="Maroon" title="c4">v</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">u2</font>
 ;<br/><b>hence </b><a NAME="E3:37_1_1"/>
<font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c5">u1</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c4">v</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c6">u2</font>
 <b>by </b><i><a class="txt" href="geomtrap.html#E5:37"><i><font color="Green" title="E39">A5</font></i></a>, <a class="txt" href="geomtrap.html#E6:37"><i><font color="Green" title="E40">A6</font></i></a>, <a class="ref" href="analoaf.html#T20" title="ANALOAF:th.20">ANALOAF:20</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="E2:37_1"/>
<font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c5">u1</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c4">v</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c6">u2</font>
 <b>by </b><i><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"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E9:37"/><i><font color="Green" title="E43">A9</font></i>: 
<font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c6">u2</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c4">v</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">u1</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_2"><b>proof </b></a><div class="add">

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_2_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:37_2_1"/>
<font color="Maroon" title="c4">v</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">v</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">u1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c6">u2</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c4">v</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">u1</font></span><br/><a NAME="E2:37_2_1"/><b>then </b>
<font color="Maroon" title="c4">v</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">u1</font>
 ;<br/><b>hence </b><a NAME="E3:37_2_1"/>
<font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c6">u2</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c4">v</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">u1</font>
 <b>by </b><i><a class="txt" href="geomtrap.html#E3:37"><i><font color="Green" title="E37">A3</font></i></a>, <a class="txt" href="geomtrap.html#E6:37"><i><font color="Green" title="E40">A6</font></i></a>, <a class="ref" href="analoaf.html#T20" title="ANALOAF:th.20">ANALOAF:20</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="E2:37_2"/>
<font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c6">u2</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c4">v</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">u1</font>
 <b>by </b><i><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"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E10:37"/><i><font color="Green" title="E44">A10</font></i>: 
( <font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c5">u1</font> <a href="geomtrap.html#R1" title="GEOMTRAP:pred.1">'||'</a> <font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c4">v</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">u1</font> &amp; <font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c6">u2</font> <a href="geomtrap.html#R1" title="GEOMTRAP:pred.1">'||'</a> <font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c4">v</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c6">u2</font> )
 
<b>by </b><i><a class="txt" href="geomtrap.html#E6:37"><i><font color="Green" title="E40">A6</font></i></a>, <a class="ref" href="geomtrap.html#D1" target="_self" title="GEOMTRAP:def.1">Def1</a></i>;<br/>
<a NAME="E11:37"/><i><font color="Green" title="E45">A11</font></i>: 
( <font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c5">u1</font> <a href="geomtrap.html#R1" title="GEOMTRAP:pred.1">'||'</a> <font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c5">u1</font> &amp; <font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c5">u1</font> <a href="geomtrap.html#R1" title="GEOMTRAP:pred.1">'||'</a> <font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c4">v</font> &amp; <font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c6">u2</font> <a href="geomtrap.html#R1" title="GEOMTRAP:pred.1">'||'</a> <font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c6">u2</font> &amp; <font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c6">u2</font> <a href="geomtrap.html#R1" title="GEOMTRAP:pred.1">'||'</a> <font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c4">v</font> )
 
<b>by </b><i><a class="txt" href="geomtrap.html#E7:37"><i><font color="Green" title="E41">A7</font></i></a>, <a class="ref" href="geomtrap.html#D1" target="_self" title="GEOMTRAP:def.1">Def1</a></i>;<br/>
<a NAME="E12:37"/><i><font color="Green" title="E46">A12</font></i>: 
<font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c5">u1</font> <a href="geomtrap.html#R1" title="GEOMTRAP:pred.1">'||'</a> <font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c4">v</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c6">u2</font>
 
<b>by </b><i><a class="txt" href="geomtrap.html#E8:37"><i><font color="Green" title="E42">A8</font></i></a>, <a class="ref" href="geomtrap.html#D1" target="_self" title="GEOMTRAP:def.1">Def1</a></i>;<br/>
<a NAME="E13:37"/><i><font color="Green" title="E47">A13</font></i>: 
<font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c6">u2</font> <a href="geomtrap.html#R1" title="GEOMTRAP:pred.1">'||'</a> <font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c4">v</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">u1</font>
 
<b>by </b><i><a class="txt" href="geomtrap.html#E9:37"><i><font color="Green" title="E43">A9</font></i></a>, <a class="ref" href="geomtrap.html#D1" target="_self" title="GEOMTRAP:def.1">Def1</a></i>;<br/>
<div><i><font color="Green" title="E48">A14</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="37_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:37_3"/><i><font color="Green" title="E49">A15</font></i>: 
<font color="Maroon" title="c4">v</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">u1</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="E2:37_3"/><b>then </b>
<font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c5">u1</font> <a href="geomtrap.html#R1" title="GEOMTRAP:pred.1">'||'</a> <font color="Maroon" title="c4">v</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">u1</font>,<font color="Maroon" title="c4">v</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c6">u2</font>
 <b>by </b><i><a class="txt" href="geomtrap.html#E1:37"><i><font color="Green" title="E35">A1</font></i></a>, <a class="txt" href="geomtrap.html#E10:37"><i><font color="Green" title="E44">A10</font></i></a>, <a class="txt" href="geomtrap.html#E11:37"><i><font color="Green" title="E45">A11</font></i></a>, <a class="txt" href="geomtrap.html#E12:37"><i><font color="Green" title="E46">A12</font></i></a>, <a class="txt" href="geomtrap.html#E38"><i><font color="Green" title="E33">Lm10</font></i></a></i>;<br/><a NAME="E3:37_3"/><b>then </b>
<font color="Maroon" title="c4">v</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">u1</font>,<font color="Maroon" title="c4">v</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c6">u2</font>,<font color="Maroon" title="c4">v</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">u1</font>,<font color="Maroon" title="c4">v</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c6">u2</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#E1:37"><i><font color="Green" title="E35">A1</font></i></a>, <a class="txt" href="geomtrap.html#E3:37"><i><font color="Green" title="E37">A3</font></i></a>, <a class="txt" href="geomtrap.html#E1:37_3"><i><font color="Green" title="E49">A15</font></i></a>, <a class="txt" href="geomtrap.html#E28"><i><font color="Green" title="E25">Lm9</font></i></a></i>;<br/><b>hence </b><a NAME="E4:37_3"/>
contradiction
 <b>by </b><i><a class="txt" href="geomtrap.html#E1:37"><i><font color="Green" title="E35">A1</font></i></a>, <a class="txt" href="geomtrap.html#E4:37"><i><font color="Green" title="E38">A4</font></i></a>, <a class="txt" href="geomtrap.html#E26"><i><font color="Green" title="E23">Lm7</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>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_4"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:37_4"/><i><font color="Green" title="E49">A16</font></i>: 
<font color="Maroon" title="c4">v</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">u2</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="E2:37_4"/><b>then </b>
<font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c6">u2</font> <a href="geomtrap.html#R1" title="GEOMTRAP:pred.1">'||'</a> <font color="Maroon" title="c4">v</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">u1</font>,<font color="Maroon" title="c4">v</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c6">u2</font>
 <b>by </b><i><a class="txt" href="geomtrap.html#E1:37"><i><font color="Green" title="E35">A1</font></i></a>, <a class="txt" href="geomtrap.html#E10:37"><i><font color="Green" title="E44">A10</font></i></a>, <a class="txt" href="geomtrap.html#E11:37"><i><font color="Green" title="E45">A11</font></i></a>, <a class="txt" href="geomtrap.html#E13:37"><i><font color="Green" title="E47">A13</font></i></a>, <a class="txt" href="geomtrap.html#E38"><i><font color="Green" title="E33">Lm10</font></i></a></i>;<br/><a NAME="E3:37_4"/><b>then </b>
<font color="Maroon" title="c4">v</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">u1</font>,<font color="Maroon" title="c4">v</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c6">u2</font>,<font color="Maroon" title="c4">v</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">u1</font>,<font color="Maroon" title="c4">v</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c6">u2</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#E1:37"><i><font color="Green" title="E35">A1</font></i></a>, <a class="txt" href="geomtrap.html#E3:37"><i><font color="Green" title="E37">A3</font></i></a>, <a class="txt" href="geomtrap.html#E1:37_4"><i><font color="Green" title="E49">A16</font></i></a>, <a class="txt" href="geomtrap.html#E28"><i><font color="Green" title="E25">Lm9</font></i></a></i>;<br/><b>hence </b><a NAME="E4:37_4"/>
contradiction
 <b>by </b><i><a class="txt" href="geomtrap.html#E1:37"><i><font color="Green" title="E35">A1</font></i></a>, <a class="txt" href="geomtrap.html#E4:37"><i><font color="Green" title="E38">A4</font></i></a>, <a class="txt" href="geomtrap.html#E26"><i><font color="Green" title="E23">Lm7</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>
<b>hence </b><a NAME="E16:37"/>
contradiction
 <b>by </b><i><a class="txt" href="geomtrap.html#E4:37"><i><font color="Green" title="E38">A4</font></i></a>, <a class="txt" href="geomtrap.html#E14:37"><i><font color="Green" title="E48">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/>


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