<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">V</font> be   <a href="rlvect_1.html#NM2">RealLinearSpace</a>;<br/><b>let </b><font color="Maroon">w</font> be   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">V</font>;<br/><b>let </b><font color="Maroon">y</font> be   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">V</font>;<br/><b>let </b><font color="Maroon">u</font> be   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">V</font>, <font color="Maroon">u'</font> be   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">V</font>, <font color="Maroon">u1</font> be   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">V</font>, <font color="Maroon">u2</font> be   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">V</font>, <font color="Maroon">v1</font> be   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">V</font>, <font color="Maroon">v2</font> be   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">V</font>, <font color="Maroon">t1</font> be   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">V</font>, <font color="Maroon">t2</font> be   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">V</font>, <font color="Maroon">w1</font> be   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">V</font>, <font color="Maroon">w2</font> be   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">V</font>;<br/>







<b>assume </b><b>that </b><br/><a NAME="E1:66"/><i><font color="Green">E45</font></i>: 
 <a href="analmetr.html#R1">Gen</a> <font color="Maroon">w</font>,<font color="Maroon">y</font>
 <b>and </b><br/><a NAME="E2:66"/><i><font color="Green">E46</font></i>: 
<font color="Maroon">u</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">u'</font>
 <b>and </b><br/><a NAME="E3:66"/><i><font color="Green">E47</font></i>: 
( <font color="Maroon">u</font>,<font color="Maroon">u'</font>,<font color="Maroon">u1</font>,<font color="Maroon">t1</font> <a href="geomtrap.html#R2" target="_self">are_DTr_wrt</a> <font color="Maroon">w</font>,<font color="Maroon">y</font> &amp; <font color="Maroon">u</font>,<font color="Maroon">u'</font>,<font color="Maroon">u2</font>,<font color="Maroon">t2</font> <a href="geomtrap.html#R2" target="_self">are_DTr_wrt</a> <font color="Maroon">w</font>,<font color="Maroon">y</font> &amp; <font color="Maroon">u</font>,<font color="Maroon">u'</font>,<font color="Maroon">v1</font>,<font color="Maroon">w1</font> <a href="geomtrap.html#R2" target="_self">are_DTr_wrt</a> <font color="Maroon">w</font>,<font color="Maroon">y</font> &amp; <font color="Maroon">u</font>,<font color="Maroon">u'</font>,<font color="Maroon">v2</font>,<font color="Maroon">w2</font> <a href="geomtrap.html#R2" target="_self">are_DTr_wrt</a> <font color="Maroon">w</font>,<font color="Maroon">y</font> )
 <b>and </b><br/><a NAME="E4:66"/><i><font color="Green">E67</font></i>: 
<font color="Maroon">u1</font>,<font color="Maroon">u2</font>,<font color="Maroon">v1</font>,<font color="Maroon">v2</font> <a href="geomtrap.html#R2" target="_self">are_DTr_wrt</a> <font color="Maroon">w</font>,<font color="Maroon">y</font>
 ;<br/>

<a NAME="E5:66"/><i><font color="Green">E72</font></i>: 
<font color="Maroon">t1</font>,<font color="Maroon">t2</font> <a href="analoaf.html#R1">//</a> <font color="Maroon">w1</font>,<font color="Maroon">w2</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="66_1"><b>proof </b></a><div class="add">

<a NAME="E1:66_1"/>
<font color="Maroon">u1</font>,<font color="Maroon">u2</font> <a href="analoaf.html#R1">//</a> <font color="Maroon">v1</font>,<font color="Maroon">v2</font>
 
<b>by </b><i><a class="txt" href="geomtrap.html#E17"><i><font color="Green">Lemma65</font></i></a>, </i>;<br/>
<b>hence </b><a NAME="E2:66_1"/>
<font color="Maroon">t1</font>,<font color="Maroon">t2</font> <a href="analoaf.html#R1">//</a> <font color="Maroon">w1</font>,<font color="Maroon">w2</font>
 <b>by </b><i><a class="ref" href="geomtrap.html#T12" target="_self">Th12</a>, <a class="ref" href="geomtrap.html#T13" target="_self">Th13</a>, <a class="ref" href="geomtrap.html#T14" target="_self">Th14</a>, </i>;<br/>


</div><b>end;</b></div>
<b>set </b><font color="Maroon">uu</font> = <font color="Maroon">u1</font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">u2</font>;<br/>
<b>set </b><font color="Maroon">vv</font> = <font color="Maroon">v1</font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">v2</font>;<br/>
<a NAME="E6:66"/><i><font color="Green">E73</font></i>: 
( <font color="Maroon">u</font>,<font color="Maroon">u'</font>,<font color="Maroon">u1</font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">u2</font>,<font color="Maroon">t1</font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">t2</font> <a href="geomtrap.html#R2" target="_self">are_DTr_wrt</a> <font color="Maroon">w</font>,<font color="Maroon">y</font> &amp; <font color="Maroon">u</font>,<font color="Maroon">u'</font>,<font color="Maroon">v1</font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">v2</font>,<font color="Maroon">w1</font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">w2</font> <a href="geomtrap.html#R2" target="_self">are_DTr_wrt</a> <font color="Maroon">w</font>,<font color="Maroon">y</font> )
 
<b>by </b><i><a class="ref" href="geomtrap.html#T12" target="_self">Th12</a>, <a class="ref" href="geomtrap.html#T13" target="_self">Th13</a>, <a class="ref" href="geomtrap.html#T14" target="_self">Th14</a>, </i>;<br/>
<a NAME="E7:66"/>
<font color="Maroon">u1</font>,<font color="Maroon">u2</font>,<font color="Maroon">u1</font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">u2</font>,<font color="Maroon">v1</font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">v2</font> <a href="analmetr.html#R3">are_Ort_wrt</a> <font color="Maroon">w</font>,<font color="Maroon">y</font>
 
<b>by </b><i><a class="txt" href="geomtrap.html#E17"><i><font color="Green">Lemma65</font></i></a>, </i>;<br/>
<a NAME="E8:66"/><b>then </b><i><font color="Green">E88</font></i>: 
<font color="Maroon">t1</font>,<font color="Maroon">t2</font>,<font color="Maroon">t1</font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">t2</font>,<font color="Maroon">w1</font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">w2</font> <a href="analmetr.html#R3">are_Ort_wrt</a> <font color="Maroon">w</font>,<font color="Maroon">y</font>
 
<b>by </b><i><a class="ref" href="geomtrap.html#T12" target="_self">Th12</a>, <a class="ref" href="geomtrap.html#T13" target="_self">Th13</a>, <a class="ref" href="geomtrap.html#T14" target="_self">Th14</a>, <a class="txt" href="geomtrap.html#E4:66"><i><font color="Green">E67</font></i></a>, <a class="ref" href="geomtrap.html#T9" target="_self">Th9</a></i>;<br/>
<a NAME="E9:66"/>
<font color="Maroon">v1</font>,<font color="Maroon">v2</font>,<font color="Maroon">u1</font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">u2</font>,<font color="Maroon">v1</font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">v2</font> <a href="analmetr.html#R3">are_Ort_wrt</a> <font color="Maroon">w</font>,<font color="Maroon">y</font>
 
<b>by </b><i><a class="txt" href="geomtrap.html#E17"><i><font color="Green">Lemma65</font></i></a>, </i>;<br/>
<a NAME="E10:66"/><b>then </b>
<font color="Maroon">w1</font>,<font color="Maroon">w2</font>,<font color="Maroon">t1</font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">t2</font>,<font color="Maroon">w1</font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">w2</font> <a href="analmetr.html#R3">are_Ort_wrt</a> <font color="Maroon">w</font>,<font color="Maroon">y</font>
 
<b>by </b><i><a class="ref" href="geomtrap.html#T12" target="_self">Th12</a>, <a class="ref" href="geomtrap.html#T13" target="_self">Th13</a>, <a class="ref" href="geomtrap.html#T14" target="_self">Th14</a>, <a class="txt" href="geomtrap.html#E4:66"><i><font color="Green">E67</font></i></a>, <a class="ref" href="geomtrap.html#T9" target="_self">Th9</a></i>;<br/>
<b>hence </b><a NAME="E11:66"/>
<font color="Maroon">t1</font>,<font color="Maroon">t2</font>,<font color="Maroon">w1</font>,<font color="Maroon">w2</font> <a href="geomtrap.html#R2" target="_self">are_DTr_wrt</a> <font color="Maroon">w</font>,<font color="Maroon">y</font>
 <b>by </b><i><a class="ref" href="geomtrap.html#T15" target="_self">Th15</a>, <a class="ref" href="geomtrap.html#T16" target="_self">Th16</a>, </i>;<br/>


</div>
