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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="rlvect_1.html#NM2">RealLinearSpace</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>





<b>assume </b><a NAME="E1:56"/><i><font color="Green">E53</font></i>: 
 <a href="analmetr.html#R1">Gen</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<b>let </b><font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font> be   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>

<b>set </b><font color="Maroon">c<sub>6</sub></font> =  <a href="geomtrap.html#K2" target="_self">pr1</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>7</sub></font> =  <a href="geomtrap.html#K3" target="_self">pr2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>8</sub></font> =  <a href="geomtrap.html#K2" target="_self">pr1</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>9</sub></font> =  <a href="geomtrap.html#K3" target="_self">pr2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font>;<br/>
<a NAME="E2:56"/><i><font color="Green">E54</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="geomtrap.html#K2" target="_self">pr1</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="geomtrap.html#K3" target="_self">pr2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="geomtrap.html#K2" target="_self">pr1</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="geomtrap.html#K3" target="_self">pr2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> )
 
<b>by </b><i><a class="txt" href="geomtrap.html#E1:56"><i><font color="Green">E53</font></i></a>, <a class="txt" href="geomtrap.html#E49"><i><font color="Green">Lemma44</font></i></a></i>;<br/>
<a NAME="E3:56"/><i><font color="Green">E55</font></i>: 
( <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analmetr.html#R2">are_Ort_wrt</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> implies  <a href="geomtrap.html#K4" target="_self">PProJ</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 0 )
 
<b>by </b><i><a class="txt" href="geomtrap.html#E1:56"><i><font color="Green">E53</font></i></a>, <a class="txt" href="geomtrap.html#E2:56"><i><font color="Green">E54</font></i></a>, <a class="ref" href="analmetr.html#T5">ANALMETR:5</a></i>;<br/>
<a NAME="E4:56"/>
(  <a href="geomtrap.html#K4" target="_self">PProJ</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 0 implies <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analmetr.html#R2">are_Ort_wrt</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> )
 
<b>by </b><i><a class="txt" href="geomtrap.html#E2:56"><i><font color="Green">E54</font></i></a>, <a class="ref" href="analmetr.html#D2">ANALMETR:def 2</a></i>;<br/>
<b>hence </b><a NAME="E5:56"/>
( <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analmetr.html#R2">are_Ort_wrt</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> iff  <a href="geomtrap.html#K4" target="_self">PProJ</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 0 )
 <b>by </b><i><a class="txt" href="geomtrap.html#E3:56"><i><font color="Green">E55</font></i></a></i>;<br/>


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