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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>assume </b><a NAME="E1:50"/><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>set </b><font color="Maroon">p</font> = <font color="Maroon">u</font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">v</font>;<br/>
2 <a href="rlvect_1.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">u</font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">v</font></span>)</span> = 
<span class="p1">(<span class="default">1 <a href="real_1.html#K3">+</a> 1</span>)</span> <a href="rlvect_1.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">u</font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">v</font></span>)</span>

<br/>.= 
<span class="p1">(<span class="default">1 <a href="rlvect_1.html#K3">*</a> <span class="p2">(<span class="default"><font color="Maroon">u</font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">v</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default">1 <a href="rlvect_1.html#K3">*</a> <span class="p2">(<span class="default"><font color="Maroon">u</font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">v</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#D9">RLVECT_1:def 9</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">u</font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">v</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default">1 <a href="rlvect_1.html#K3">*</a> <span class="p2">(<span class="default"><font color="Maroon">u</font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">v</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#D9">RLVECT_1:def 9</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">u</font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">v</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">u</font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">v</font></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#D9">RLVECT_1:def 9</a></i>
<br/>.= 
<font color="Maroon">u</font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">v</font>
<b>by </b><i/>
;<br/>
<a NAME="E3:50"/><b>then </b>
( 2 <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="geomtrap.html#K2" target="_self">pr1</a> <font color="Maroon">w</font>,<font color="Maroon">y</font>,<span class="p2">(<span class="default"><font color="Maroon">u</font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">v</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="geomtrap.html#K2" target="_self">pr1</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#K4">+</a> <font color="Maroon">v</font></span>)</span> &amp; 2 <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="geomtrap.html#K3" target="_self">pr2</a> <font color="Maroon">w</font>,<font color="Maroon">y</font>,<span class="p2">(<span class="default"><font color="Maroon">u</font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">v</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="geomtrap.html#K3" target="_self">pr2</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#K4">+</a> <font color="Maroon">v</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="geomtrap.html#T3" target="_self">Th3</a>, </i>;<br/>
<b>hence </b><a NAME="E4:50"/>
( 2 <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="geomtrap.html#K2" target="_self">pr1</a> <font color="Maroon">w</font>,<font color="Maroon">y</font>,<span class="p2">(<span class="default"><font color="Maroon">u</font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">v</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="geomtrap.html#K2" target="_self">pr1</a> <font color="Maroon">w</font>,<font color="Maroon">y</font>,<font color="Maroon">u</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><a href="geomtrap.html#K2" target="_self">pr1</a> <font color="Maroon">w</font>,<font color="Maroon">y</font>,<font color="Maroon">v</font></span>)</span> &amp; 2 <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="geomtrap.html#K3" target="_self">pr2</a> <font color="Maroon">w</font>,<font color="Maroon">y</font>,<span class="p2">(<span class="default"><font color="Maroon">u</font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">v</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="geomtrap.html#K3" target="_self">pr2</a> <font color="Maroon">w</font>,<font color="Maroon">y</font>,<font color="Maroon">u</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><a href="geomtrap.html#K3" target="_self">pr2</a> <font color="Maroon">w</font>,<font color="Maroon">y</font>,<font color="Maroon">v</font></span>)</span> )
 <b>by </b><i><a class="ref" href="geomtrap.html#T3" target="_self">Th3</a>, </i>;<br/>


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