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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">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>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/>
<a NAME="E1:12"/><i><font color="Green">E45</font></i>: 
2 <a href="real_1.html#K5">-</a> 1 <a href="hidden.html#R1">=</a> 1
 
;<br/>
<a NAME="E2:12"/><i><font color="Green">E46</font></i>: 
1 <a href="real_1.html#K5">-</a> 2 <a href="hidden.html#R1">=</a>  <a href="real_1.html#K1">-</a> 1
 
;<br/>
<i><font color="Green">E47</font></i>: 2 <a href="rlvect_1.html#K3">*</a> <span class="p1">(<span class="default"><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> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">u</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> 1</span>)</span> <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#K6">-</a> <span class="p1">(<span class="default">2 <a href="rlvect_1.html#K3">*</a> <font color="Maroon">u</font></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#T48">RLVECT_1:48</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="rlvect_1.html#K3">*</a> <span class="p3">(<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="p2">(<span class="default">1 <a href="rlvect_1.html#K3">*</a> <span class="p3">(<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></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default">2 <a href="rlvect_1.html#K3">*</a> <font color="Maroon">u</font></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"><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> <a href="rlvect_1.html#K4">+</a> <span class="p2">(<span class="default">1 <a href="rlvect_1.html#K3">*</a> <span class="p3">(<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></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default">2 <a href="rlvect_1.html#K3">*</a> <font color="Maroon">u</font></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"><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> <a href="rlvect_1.html#K4">+</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#K6">-</a> <span class="p1">(<span class="default">2 <a href="rlvect_1.html#K3">*</a> <font color="Maroon">u</font></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="rlvect_1.html#K4">+</a> <font color="Maroon">v</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default">2 <a href="rlvect_1.html#K3">*</a> <font color="Maroon">u</font></span>)</span>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">v</font> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">u</font> <a href="rlvect_1.html#K6">-</a> <span class="p2">(<span class="default">2 <a href="rlvect_1.html#K3">*</a> <font color="Maroon">u</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#D6">RLVECT_1:def 6</a></i>
<br/>.= 
<font color="Maroon">v</font> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="rlvect_1.html#K3">*</a> <font color="Maroon">u</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p2">(<span class="default">2 <a href="rlvect_1.html#K3">*</a> <font color="Maroon">u</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#D9">RLVECT_1:def 9</a></i>
<br/>.= 
<font color="Maroon">v</font> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">u</font></span>)</span>
<b>by </b><i>, <a class="ref" href="rlvect_1.html#T49">RLVECT_1:49</a></i>
<br/>.= 
<font color="Maroon">v</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">u</font>
<b>by </b><i><a class="ref" href="rlvect_1.html#T29">RLVECT_1:29</a></i>
;<br/>
2 <a href="rlvect_1.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">v</font> <a href="rlvect_1.html#K6">-</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> = 
<span class="p1">(<span class="default">2 <a href="rlvect_1.html#K3">*</a> <font color="Maroon">v</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> 1</span>)</span> <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#T48">RLVECT_1:48</a></i>
<br/>.= 
<span class="p1">(<span class="default">2 <a href="rlvect_1.html#K3">*</a> <font color="Maroon">v</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="rlvect_1.html#K3">*</a> <span class="p3">(<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="p2">(<span class="default">1 <a href="rlvect_1.html#K3">*</a> <span class="p3">(<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></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">2 <a href="rlvect_1.html#K3">*</a> <font color="Maroon">v</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="rlvect_1.html#K3">*</a> <span class="p3">(<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="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">2 <a href="rlvect_1.html#K3">*</a> <font color="Maroon">v</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><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> <a href="rlvect_1.html#K4">+</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">2 <a href="rlvect_1.html#K3">*</a> <font color="Maroon">v</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <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/>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="rlvect_1.html#K3">*</a> <font color="Maroon">v</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">v</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">u</font>
<b>by </b><i><a class="ref" href="rlvect_1.html#T41">RLVECT_1:41</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="rlvect_1.html#K3">*</a> <font color="Maroon">v</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p2">(<span class="default">1 <a href="rlvect_1.html#K3">*</a> <font color="Maroon">v</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">u</font>
<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">1 <a href="rlvect_1.html#K3">*</a> <font color="Maroon">v</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">u</font>
<b>by </b><i>, <a class="ref" href="rlvect_1.html#T49">RLVECT_1:49</a></i>
<br/>.= 
<font color="Maroon">v</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">u</font>
<b>by </b><i><a class="ref" href="rlvect_1.html#D9">RLVECT_1:def 9</a></i>
;<br/>
<b>hence </b><a NAME="E5:12"/>
( 2 <a href="rlvect_1.html#K3">*</a> <span class="p1">(<span class="default"><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> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">u</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">v</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">u</font> &amp; 2 <a href="rlvect_1.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">v</font> <a href="rlvect_1.html#K6">-</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="hidden.html#R1">=</a> <font color="Maroon">v</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">u</font> )
 <b>by </b><i/>;<br/>


</div>
