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<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>let </b><font color="Maroon">u2</font> be   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">V</font>;<br/><b>let </b><font color="Maroon">v2</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="E1:31"/><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="E2:31"/><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> &amp; <font color="Maroon">u</font>,<font color="Maroon">v</font>,<font color="Maroon">u2</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> )
 <b>and </b><br/><a NAME="E3:31"/><i><font color="Green">E47</font></i>: 
<font color="Maroon">u</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">v</font>
 ;<br/>

<a NAME="E4:31"/><i><font color="Green">E67</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/>
<a NAME="E5:31"/><i><font color="Green">E72</font></i>: 
( <font color="Maroon">u</font>,<font color="Maroon">v</font> <a href="analoaf.html#R1">//</a> <font color="Maroon">u2</font>,<font color="Maroon">v2</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">u2</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> &amp; <font color="Maroon">u2</font>,<font color="Maroon">v2</font>,<font color="Maroon">u</font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">v</font>,<font color="Maroon">u2</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>, </i>;<br/>
<a NAME="E6:31"/><b>then </b><i><font color="Green">E73</font></i>: 
( <font color="Maroon">u</font>,<font color="Maroon">v</font> <a href="geomtrap.html#R1" target="_self">'||'</a> <font color="Maroon">u2</font>,<font color="Maroon">v2</font> &amp; <font color="Maroon">u</font>,<font color="Maroon">v</font> <a href="geomtrap.html#R1" target="_self">'||'</a> <font color="Maroon">u1</font>,<font color="Maroon">v1</font> )
 
<b>by </b><i>, </i>;<br/>
<a NAME="E7:31"/><i><font color="Green">E88</font></i>: 
<font color="Maroon">u1</font>,<font color="Maroon">v1</font> <a href="analoaf.html#R1">//</a> <font color="Maroon">u2</font>,<font color="Maroon">v2</font>
 
<b>by </b><i>, , , <a class="ref" href="analoaf.html#T20">ANALOAF:20</a></i>;<br/>
<b>set </b><font color="Maroon">a</font> = <font color="Maroon">u1</font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">v1</font>;<br/>
<b>set </b><font color="Maroon">b</font> = <font color="Maroon">u2</font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">v2</font>;<br/>
<a NAME="E8:31"/>
<font color="Maroon">u</font>,<font color="Maroon">v</font>,<font color="Maroon">u1</font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">v1</font>,<font color="Maroon">u2</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>, , , </i>;<br/>
<a NAME="E9:31"/><b>then </b>
( <font color="Maroon">u1</font>,<font color="Maroon">v1</font>,<font color="Maroon">u1</font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">v1</font>,<font color="Maroon">u2</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> &amp; <font color="Maroon">u2</font>,<font color="Maroon">v2</font>,<font color="Maroon">u1</font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">v1</font>,<font color="Maroon">u2</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>, , , </i>;<br/>
<b>hence </b><a NAME="E10:31"/>
<font color="Maroon">u1</font>,<font color="Maroon">v1</font>,<font color="Maroon">u2</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>
 <b>by </b><i>, </i>;<br/>


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