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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> 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="E1:56"/><i><font color="Green" title="E53">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>let </b><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>set </b><font color="Maroon" title="c6">a1</font> =  <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>;<br/>
<b>set </b><font color="Maroon" title="c7">a2</font> =  <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>;<br/>
<b>set </b><font color="Maroon" title="c8">b1</font> =  <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>;<br/>
<b>set </b><font color="Maroon" title="c9">b2</font> =  <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>;<br/>
<a NAME="E2:56"/><i><font color="Green" title="E54">A2</font></i>: 
( <font color="Maroon" title="c4">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<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="rlvect_1.html#K3" title="RLVECT_1:func.3">*</a> <font color="Maroon" title="c2">w</font></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">+</a> <span class="p1">(<span class="default"><span class="p2">(<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="rlvect_1.html#K3" title="RLVECT_1:func.3">*</a> <font color="Maroon" title="c3">y</font></span>)</span> &amp; <font color="Maroon" title="c5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<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> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">*</a> <font color="Maroon" title="c2">w</font></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">+</a> <span class="p1">(<span class="default"><span class="p2">(<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> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">*</a> <font color="Maroon" title="c3">y</font></span>)</span> )
 
<b>by </b><i><a class="txt" href="geomtrap.html#E1:56"><i><font color="Green" title="E53">A1</font></i></a>, <a class="txt" href="geomtrap.html#E49"><i><font color="Green" title="E44">Lm14</font></i></a></i>;<br/>
<a NAME="E3:56"/><i><font color="Green" title="E55">A3</font></i>: 
( <font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font> <a href="analmetr.html#R2" title="ANALMETR:pred.2">are_Ort_wrt</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font> implies  <a href="geomtrap.html#K4" title="GEOMTRAP:func.4">PProJ</a> <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> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0 )
 
<b>by </b><i><a class="txt" href="geomtrap.html#E1:56"><i><font color="Green" title="E53">A1</font></i></a>, <a class="txt" href="geomtrap.html#E2:56"><i><font color="Green" title="E54">A2</font></i></a>, <a class="ref" href="analmetr.html#T5" title="ANALMETR:th.5">ANALMETR:5</a></i>;<br/>
<a NAME="E4:56"/>
(  <a href="geomtrap.html#K4" title="GEOMTRAP:func.4">PProJ</a> <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> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0 implies <font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font> <a href="analmetr.html#R2" title="ANALMETR:pred.2">are_Ort_wrt</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font> )
 
<b>by </b><i><a class="txt" href="geomtrap.html#E2:56"><i><font color="Green" title="E54">A2</font></i></a>, <a class="ref" href="analmetr.html#D2" title="ANALMETR:def.2">ANALMETR:def 2</a></i>;<br/>
<b>hence </b><a NAME="E5:56"/>
( <font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font> <a href="analmetr.html#R2" title="ANALMETR:pred.2">are_Ort_wrt</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">y</font> iff  <a href="geomtrap.html#K4" title="GEOMTRAP:func.4">PProJ</a> <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> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0 )
 <b>by </b><i><a class="txt" href="geomtrap.html#E3:56"><i><font color="Green" title="E55">A3</font></i></a></i>;<br/>


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