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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>assume </b><a NAME="E1:59"/><i><font color="Green">E45</font></i>: 
 <a href="analmetr.html#R1">Gen</a> <font color="Maroon">w</font>,<font color="Maroon">y</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">v</font> be   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">V</font>;<br/>

<b>assume </b><a NAME="E2:59"/><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">v</font>
 ;<br/>

<b>assume </b><a NAME="E3:59"/>
 <a href="geomtrap.html#K4" target="_self">PProJ</a> <font color="Maroon">w</font>,<font color="Maroon">y</font>,<span class="p1">(<span class="default"><font color="Maroon">u</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">v</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">u</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">v</font></span>)</span> <a href="hidden.html#R1">=</a> 0
 ;<br/>

<a NAME="E4:59"/><b>then </b>
<font color="Maroon">u</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">v</font>,<font color="Maroon">u</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">v</font> <a href="analmetr.html#R2">are_Ort_wrt</a> <font color="Maroon">w</font>,<font color="Maroon">y</font>
 
<b>by </b><i><a class="ref" href="geomtrap.html#T7" target="_self">Th7</a>, </i>;<br/>
<a NAME="E5:59"/><b>then </b>
<font color="Maroon">u</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">v</font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">V</font>
 
<b>by </b><i><a class="ref" href="geomtrap.html#T7" target="_self">Th7</a>, <a class="ref" href="analmetr.html#T15">ANALMETR:15</a></i>;<br/>
<b>hence </b><a NAME="E6:59"/>
contradiction
 <b>by </b><i><a class="ref" href="geomtrap.html#T8" target="_self">Th8</a>, <a class="ref" href="rlvect_1.html#T35">RLVECT_1:35</a></i>;<br/>


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