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<b>let </b><font color="Maroon" title="c1">V</font> be   <a href="rlvect_1.html#NM2" title="RLVECT_1:NM.2">RealLinearSpace</a>;<br/><b>let </b><font color="Maroon" title="c2">w</font>, <font color="Maroon" title="c3">y</font>, <font color="Maroon" title="c4">u</font>, <font color="Maroon" title="c5">v</font> be   <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font>;<br/>









<b>assume </b><a NAME="E1:50"/><i><font color="Green" title="E48">A1</font></i>: 
 <a href="analmetr.html#R1" title="ANALMETR:pred.1">Gen</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>
 ;<br/>

<b>set </b><font color="Maroon" title="c6">p</font> = <font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font>;<br/>
2 <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font></span>)</span> = 
<span class="p1">(<span class="default">1 <a href="real_1.html#K3" title="REAL_1:func.3">+</a> 1</span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font></span>)</span>

<br/>.= 
<span class="p1">(<span class="default">1 <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">+</a> <span class="p1">(<span class="default">1 <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#D9" title="RLVECT_1:def.9">RLVECT_1:def 9</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">+</a> <span class="p1">(<span class="default">1 <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#D9" title="RLVECT_1:def.9">RLVECT_1:def 9</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#D9" title="RLVECT_1:def.9">RLVECT_1:def 9</a></i>
<br/>.= 
<font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">+</a> <font color="Maroon" title="c5">v</font>
<b>by </b><i><a class="ref" href="geomtrap.html#D2" target="_self" title="GEOMTRAP:def.2">Def2</a></i>
;<br/>
<a NAME="E3:50"/><b>then </b>
( 2 <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p1">(<span class="default"><a href="geomtrap.html#K2" title="GEOMTRAP:func.2">pr1</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="geomtrap.html#K2" title="GEOMTRAP:func.2">pr1</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">+</a> <font color="Maroon" title="c5">v</font></span>)</span> &amp; 2 <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p1">(<span class="default"><a href="geomtrap.html#K3" title="GEOMTRAP:func.3">pr2</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="geomtrap.html#K3" title="GEOMTRAP:func.3">pr2</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">+</a> <font color="Maroon" title="c5">v</font></span>)</span> )
 
<b>by </b><i><a class="txt" href="geomtrap.html#E1:50"><i><font color="Green" title="E48">A1</font></i></a>, <a class="txt" href="geomtrap.html#E51"><i><font color="Green" title="E46">Lm16</font></i></a></i>;<br/>
<b>hence </b><a NAME="E4:50"/>
( 2 <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p1">(<span class="default"><a href="geomtrap.html#K2" title="GEOMTRAP:func.2">pr1</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="geomtrap.html#K2" title="GEOMTRAP:func.2">pr1</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">u</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p1">(<span class="default"><a href="geomtrap.html#K2" title="GEOMTRAP:func.2">pr1</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c5">v</font></span>)</span> &amp; 2 <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p1">(<span class="default"><a href="geomtrap.html#K3" title="GEOMTRAP:func.3">pr2</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c5">v</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="geomtrap.html#K3" title="GEOMTRAP:func.3">pr2</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">u</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p1">(<span class="default"><a href="geomtrap.html#K3" title="GEOMTRAP:func.3">pr2</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c5">v</font></span>)</span> )
 <b>by </b><i><a class="txt" href="geomtrap.html#E1:50"><i><font color="Green" title="E48">A1</font></i></a>, <a class="txt" href="geomtrap.html#E51"><i><font color="Green" title="E46">Lm16</font></i></a></i>;<br/>


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