<?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>;<br/><b>let </b><font color="Maroon">v</font> be   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">V</font>;<br/><b>let </b><font color="Maroon">u1</font> be   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">V</font>;<br/><b>let </b><font color="Maroon">v1</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="E1:34"/><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="E2:34"/><i><font color="Green">E46</font></i>: 
<font color="Maroon">u</font>,<font color="Maroon">v</font>,<font color="Maroon">u1</font>,<font color="Maroon">v1</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="E3:34"/><i><font color="Green">E47</font></i>: 
( <font color="Maroon">u</font>,<font color="Maroon">v</font> <a href="analoaf.html#R1">//</a> <font color="Maroon">u1</font>,<font color="Maroon">v1</font> &amp; <font color="Maroon">u</font>,<font color="Maroon">v</font>,<font color="Maroon">u</font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">v</font>,<font color="Maroon">u1</font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">v1</font> <a href="analmetr.html#R3">are_Ort_wrt</a> <font color="Maroon">w</font>,<font color="Maroon">y</font> &amp; <font color="Maroon">u1</font>,<font color="Maroon">v1</font>,<font color="Maroon">u</font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">v</font>,<font color="Maroon">u1</font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">v1</font> <a href="analmetr.html#R3">are_Ort_wrt</a> <font color="Maroon">w</font>,<font color="Maroon">y</font> )
 
<b>by </b><i>, </i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="34_1"><b>now </b></a><div class="add"><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">v</font> be   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">V</font>, <font color="Maroon">v'</font> be   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">V</font>;<br/><b>assume </b><a NAME="E1:34_1"/>
<font color="Maroon">u</font>,<font color="Maroon">u'</font>,<font color="Maroon">v</font>,<font color="Maroon">v'</font> <a href="analmetr.html#R3">are_Ort_wrt</a> <font color="Maroon">w</font>,<font color="Maroon">y</font>
 ;<br/><a NAME="E2:34_1"/><b>then </b>
<font color="Maroon">v</font>,<font color="Maroon">v'</font>,<font color="Maroon">u</font>,<font color="Maroon">u'</font> <a href="analmetr.html#R3">are_Ort_wrt</a> <font color="Maroon">w</font>,<font color="Maroon">y</font>
 <b>by </b><i>, </i>;<br/><a NAME="E3:34_1"/><b>then </b>
<font color="Maroon">v</font>,<font color="Maroon">v'</font>,<font color="Maroon">u'</font>,<font color="Maroon">u</font> <a href="analmetr.html#R3">are_Ort_wrt</a> <font color="Maroon">w</font>,<font color="Maroon">y</font>
 <b>by </b><i>, </i>;<br/><b>hence </b><a NAME="E4:34_1"/>
<font color="Maroon">u'</font>,<font color="Maroon">u</font>,<font color="Maroon">v</font>,<font color="Maroon">v'</font> <a href="analmetr.html#R3">are_Ort_wrt</a> <font color="Maroon">w</font>,<font color="Maroon">y</font>
 <b>by </b><i>, </i>;<br/></div><b>end;</b></div>
<a NAME="E5:34"/><b>then </b>
( <font color="Maroon">v</font>,<font color="Maroon">u</font> <a href="analoaf.html#R1">//</a> <font color="Maroon">v1</font>,<font color="Maroon">u1</font> &amp; <font color="Maroon">v</font>,<font color="Maroon">u</font>,<font color="Maroon">v</font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">u</font>,<font color="Maroon">v1</font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">u1</font> <a href="analmetr.html#R3">are_Ort_wrt</a> <font color="Maroon">w</font>,<font color="Maroon">y</font> &amp; <font color="Maroon">v1</font>,<font color="Maroon">u1</font>,<font color="Maroon">v</font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">u</font>,<font color="Maroon">v1</font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">u1</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="analoaf.html#T21">ANALOAF:21</a></i>;<br/>
<b>hence </b><a NAME="E6:34"/>
<font color="Maroon">v</font>,<font color="Maroon">u</font>,<font color="Maroon">v1</font>,<font color="Maroon">u1</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/>;<br/>


</div>
