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<b>let </b><font color="Maroon">MS</font> be   <a href="analmetr.html#NM2">OrtAfPl</a>;<br/><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>assume </b><b>that </b><br/><a NAME="E1:36"/><i><font color="Green">E34</font></i>: 
 <a href="analmetr.html#R1">Gen</a> <font color="Maroon">w</font>,<font color="Maroon">y</font>
 <b>and </b><br/><a NAME="E2:36"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">MS</font> <a href="hidden.html#R1">=</a>  <a href="analmetr.html#K2">AMSpace</a> <font color="Maroon">V</font>,<font color="Maroon">w</font>,<font color="Maroon">y</font>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="36_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">o</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">MS</font>, <font color="Maroon">a</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">MS</font>, <font color="Maroon">a1</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">MS</font>, <font color="Maroon">b</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">MS</font>, <font color="Maroon">b1</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">MS</font>, <font color="Maroon">c</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">MS</font>, <font color="Maroon">c1</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">MS</font>;<br/><b>assume </b><b>that </b><br/><a NAME="E1:36_1"/><i><font color="Green">E44</font></i>: 
( <font color="Maroon">o</font>,<font color="Maroon">a</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">o</font>,<font color="Maroon">a1</font> &amp; <font color="Maroon">o</font>,<font color="Maroon">b</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">o</font>,<font color="Maroon">b1</font> &amp; <font color="Maroon">o</font>,<font color="Maroon">c</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">o</font>,<font color="Maroon">c1</font> )
 <b>and </b><br/><a NAME="E2:36_1"/><i><font color="Green">E48</font></i>: 
( <font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">a1</font>,<font color="Maroon">b1</font> &amp; <font color="Maroon">a</font>,<font color="Maroon">c</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">a1</font>,<font color="Maroon">c1</font> )
 <b>and </b><br/><a NAME="E3:36_1"/><i><font color="Green">E51</font></i>: 
( not <font color="Maroon">o</font>,<font color="Maroon">c</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o</font>,<font color="Maroon">a</font> &amp; not <font color="Maroon">o</font>,<font color="Maroon">a</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o</font>,<font color="Maroon">b</font> )
 ;<br/><b>reconsider </b><font color="Maroon">q</font> = <font color="Maroon">o</font>, <font color="Maroon">u1</font> = <font color="Maroon">a</font>, <font color="Maroon">u2</font> = <font color="Maroon">b</font>, <font color="Maroon">u3</font> = <font color="Maroon">c</font>, <font color="Maroon">v1</font> = <font color="Maroon">a1</font>, <font color="Maroon">v2</font> = <font color="Maroon">b1</font>, <font color="Maroon">v3</font> = <font color="Maroon">c1</font> as   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">V</font> <b>by </b><i><a class="txt" href="euclmetr.html#E1:36"><i><font color="Green">E34</font></i></a>, <a class="ref" href="analmetr.html#T28">ANALMETR:28</a></i>;<br/><a NAME="E5:36_1"/><i><font color="Green">E64</font></i>: 
( not  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">o</font>,<font color="Maroon">a</font>,<font color="Maroon">b</font> &amp; not  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">o</font>,<font color="Maroon">a</font>,<font color="Maroon">c</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="36_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:36_1_1"/>
(  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">o</font>,<font color="Maroon">a</font>,<font color="Maroon">b</font> or  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">o</font>,<font color="Maroon">a</font>,<font color="Maroon">c</font> )
 ;<br/>

<a NAME="E2:36_1_1"/><b>then </b>
( <font color="Maroon">o</font>,<font color="Maroon">a</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o</font>,<font color="Maroon">b</font> or <font color="Maroon">o</font>,<font color="Maroon">a</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o</font>,<font color="Maroon">c</font> )
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<b>hence </b><a NAME="E3:36_1_1"/>
contradiction
 <b>by </b><i>, <a class="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/>


</div><b>end;</b></div><a NAME="E6:36_1"/><b>then </b><i><font color="Green">E66</font></i>: 
( <font color="Maroon">o</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">a</font> &amp; <font color="Maroon">o</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b</font> &amp; <font color="Maroon">o</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c</font> )
 <b>by </b><i/>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="36_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:36_1_2"/><i><font color="Green">E67</font></i>: 
<font color="Maroon">o</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">a1</font>
 ;<br/><a NAME="E2:36_1_2"/>
( <font color="Maroon">q</font>,<font color="Maroon">u3</font>,<font color="Maroon">q</font>,<font color="Maroon">v3</font> <a href="analmetr.html#R3">are_Ort_wrt</a> <font color="Maroon">w</font>,<font color="Maroon">y</font> &amp; <font color="Maroon">q</font>,<font color="Maroon">u1</font>,<font color="Maroon">q</font>,<font color="Maroon">v1</font> <a href="analmetr.html#R3">are_Ort_wrt</a> <font color="Maroon">w</font>,<font color="Maroon">y</font> &amp; <font color="Maroon">q</font>,<font color="Maroon">u2</font>,<font color="Maroon">q</font>,<font color="Maroon">v2</font> <a href="analmetr.html#R3">are_Ort_wrt</a> <font color="Maroon">w</font>,<font color="Maroon">y</font> )
 <b>by </b><i><a class="txt" href="euclmetr.html#E1:36"><i><font color="Green">E34</font></i></a>, <a class="txt" href="euclmetr.html#E2:36"><i><font color="Green">E35</font></i></a>, <a class="ref" href="analmetr.html#T31">ANALMETR:31</a></i>;<br/><a NAME="E3:36_1_2"/><b>then </b><i><font color="Green">E69</font></i>: 
( <font color="Maroon">u1</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">q</font>,<font color="Maroon">v1</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">q</font> <a href="analmetr.html#R2">are_Ort_wrt</a> <font color="Maroon">w</font>,<font color="Maroon">y</font> &amp; <font color="Maroon">u2</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">q</font>,<font color="Maroon">v2</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">q</font> <a href="analmetr.html#R2">are_Ort_wrt</a> <font color="Maroon">w</font>,<font color="Maroon">y</font> &amp; <font color="Maroon">u3</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">q</font>,<font color="Maroon">v3</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">q</font> <a href="analmetr.html#R2">are_Ort_wrt</a> <font color="Maroon">w</font>,<font color="Maroon">y</font> )
 <b>by </b><i><a class="ref" href="analmetr.html#D3">ANALMETR:def 3</a></i>;<br/><a NAME="E4:36_1_2"/>
( <font color="Maroon">u1</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">q</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">V</font> &amp; <font color="Maroon">v1</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">q</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">V</font> )
 <b>by </b><i><a class="ref" href="euclmetr.html#T2" target="_self">Th2</a>, , <a class="ref" href="rlvect_1.html#T35">RLVECT_1:35</a></i>;<br/><b>then consider </b><font color="Maroon">r</font> being   <a href="real_1.html#NM1">Real</a><b> such that </b><br/><a NAME="E6:36_1_2"/><i><font color="Green">E77</font></i>: 
for <font color="Olive">a'</font>, <font color="Olive">b'</font> being  <a href="real_1.html#NM1">Real</a> holds <br/> ( <span class="p1">(<span class="default"><font color="Olive">a'</font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">w</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Olive">b'</font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">y</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">r</font> <a href="real_1.html#K4">*</a> <font color="Olive">b'</font></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">w</font></span>)</span> <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> <span class="p3">(<span class="default"><font color="Maroon">r</font> <a href="real_1.html#K4">*</a> <font color="Olive">a'</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">y</font></span>)</span> <a href="analmetr.html#R2">are_Ort_wrt</a> <font color="Maroon">w</font>,<font color="Maroon">y</font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive">a'</font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">w</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p2">(<span class="default"><font color="Olive">b'</font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">u1</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">q</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">r</font> <a href="real_1.html#K4">*</a> <font color="Olive">b'</font></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">w</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p4">(<span class="default"><font color="Maroon">r</font> <a href="real_1.html#K4">*</a> <font color="Olive">a'</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">v1</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">q</font></span>)</span> <a href="analmetr.html#R2">are_Ort_wrt</a> <font color="Maroon">w</font>,<font color="Maroon">y</font> )
 <b>by </b><i><a class="ref" href="euclmetr.html#T1" target="_self">Th1</a>, , </i>;<br/><b>consider </b><font color="Maroon">A1</font> being   <a href="real_1.html#NM1">Real</a>, <font color="Maroon">A2</font> being   <a href="real_1.html#NM1">Real</a><b> such that </b><br/><a NAME="E8:36_1_2"/><i><font color="Green">E80</font></i>: 
<font color="Maroon">u3</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">q</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">A1</font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">w</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">A2</font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">y</font></span>)</span>
 <b>by </b><i><a class="ref" href="euclmetr.html#T1" target="_self">Th1</a>, <a class="ref" href="analmetr.html#D1">ANALMETR:def 1</a></i>;<br/><b>consider </b><font color="Maroon">B1</font> being   <a href="real_1.html#NM1">Real</a>, <font color="Maroon">B2</font> being   <a href="real_1.html#NM1">Real</a><b> such that </b><br/><a NAME="E10:36_1_2"/><i><font color="Green">E81</font></i>: 
<font color="Maroon">u2</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">q</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">B1</font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">w</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">B2</font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">y</font></span>)</span>
 <b>by </b><i><a class="ref" href="euclmetr.html#T1" target="_self">Th1</a>, <a class="ref" href="analmetr.html#D1">ANALMETR:def 1</a></i>;<br/><b>set </b><font color="Maroon">v3'</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">r</font> <a href="real_1.html#K4">*</a> <font color="Maroon">A2</font></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">w</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p4">(<span class="default"><font color="Maroon">r</font> <a href="real_1.html#K4">*</a> <font color="Maroon">A1</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">q</font>;<br/><b>set </b><font color="Maroon">v2'</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">r</font> <a href="real_1.html#K4">*</a> <font color="Maroon">B2</font></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">w</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p4">(<span class="default"><font color="Maroon">r</font> <a href="real_1.html#K4">*</a> <font color="Maroon">B1</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">q</font>;<br/><b>reconsider </b><font color="Maroon">c1'</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">r</font> <a href="real_1.html#K4">*</a> <font color="Maroon">A2</font></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">w</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p4">(<span class="default"><font color="Maroon">r</font> <a href="real_1.html#K4">*</a> <font color="Maroon">A1</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">q</font>, <font color="Maroon">b1'</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">r</font> <a href="real_1.html#K4">*</a> <font color="Maroon">B2</font></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">w</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p4">(<span class="default"><font color="Maroon">r</font> <a href="real_1.html#K4">*</a> <font color="Maroon">B1</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">q</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">MS</font> <b>by </b><i><a class="txt" href="euclmetr.html#E1:36"><i><font color="Green">E34</font></i></a>, <a class="ref" href="analmetr.html#T28">ANALMETR:28</a></i>;<br/><a NAME="E12:36_1_2"/><i><font color="Green">E82</font></i>: 
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">r</font> <a href="real_1.html#K4">*</a> <font color="Maroon">A2</font></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">w</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p5">(<span class="default"><font color="Maroon">r</font> <a href="real_1.html#K4">*</a> <font color="Maroon">A1</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">q</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">q</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">r</font> <a href="real_1.html#K4">*</a> <font color="Maroon">A2</font></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">w</font></span>)</span> <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> <span class="p3">(<span class="default"><font color="Maroon">r</font> <a href="real_1.html#K4">*</a> <font color="Maroon">A1</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">y</font></span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">r</font> <a href="real_1.html#K4">*</a> <font color="Maroon">B2</font></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">w</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p5">(<span class="default"><font color="Maroon">r</font> <a href="real_1.html#K4">*</a> <font color="Maroon">B1</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">q</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">q</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">r</font> <a href="real_1.html#K4">*</a> <font color="Maroon">B2</font></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">w</font></span>)</span> <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> <span class="p3">(<span class="default"><font color="Maroon">r</font> <a href="real_1.html#K4">*</a> <font color="Maroon">B1</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">y</font></span>)</span> )
 <b>by </b><i><a class="ref" href="rlsub_2.html#T78">RLSUB_2:78</a></i>;<br/><a NAME="E13:36_1_2"/><b>then </b>
( <font color="Maroon">u3</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">q</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">r</font> <a href="real_1.html#K4">*</a> <font color="Maroon">A2</font></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">w</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p5">(<span class="default"><font color="Maroon">r</font> <a href="real_1.html#K4">*</a> <font color="Maroon">A1</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">q</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">q</font> <a href="analmetr.html#R2">are_Ort_wrt</a> <font color="Maroon">w</font>,<font color="Maroon">y</font> &amp; <font color="Maroon">u2</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">q</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">r</font> <a href="real_1.html#K4">*</a> <font color="Maroon">B2</font></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">w</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p5">(<span class="default"><font color="Maroon">r</font> <a href="real_1.html#K4">*</a> <font color="Maroon">B1</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">q</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">q</font> <a href="analmetr.html#R2">are_Ort_wrt</a> <font color="Maroon">w</font>,<font color="Maroon">y</font> )
 <b>by </b><i>, , <a class="txt" href="euclmetr.html#E1:36_1"><i><font color="Green">E44</font></i></a></i>;<br/><a NAME="E14:36_1_2"/><b>then </b>
( <font color="Maroon">q</font>,<font color="Maroon">u3</font>,<font color="Maroon">q</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">r</font> <a href="real_1.html#K4">*</a> <font color="Maroon">A2</font></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">w</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p4">(<span class="default"><font color="Maroon">r</font> <a href="real_1.html#K4">*</a> <font color="Maroon">A1</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">q</font> <a href="analmetr.html#R3">are_Ort_wrt</a> <font color="Maroon">w</font>,<font color="Maroon">y</font> &amp; <font color="Maroon">q</font>,<font color="Maroon">u2</font>,<font color="Maroon">q</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">r</font> <a href="real_1.html#K4">*</a> <font color="Maroon">B2</font></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">w</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p4">(<span class="default"><font color="Maroon">r</font> <a href="real_1.html#K4">*</a> <font color="Maroon">B1</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">q</font> <a href="analmetr.html#R3">are_Ort_wrt</a> <font color="Maroon">w</font>,<font color="Maroon">y</font> )
 <b>by </b><i><a class="ref" href="analmetr.html#D3">ANALMETR:def 3</a></i>;<br/><a NAME="E15:36_1_2"/><b>then </b><i><font color="Green">E97</font></i>: 
( <font color="Maroon">o</font>,<font color="Maroon">c</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">o</font>,<font color="Maroon">c1'</font> &amp; <font color="Maroon">o</font>,<font color="Maroon">b</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">o</font>,<font color="Maroon">b1'</font> )
 <b>by </b><i><a class="txt" href="euclmetr.html#E1:36"><i><font color="Green">E34</font></i></a>, <a class="ref" href="analmetr.html#T31">ANALMETR:31</a></i>;<br/><a NAME="E16:36_1_2"/>
( <span class="p1">(<span class="default"><font color="Maroon">u3</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">q</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">u1</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">q</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">u3</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">u1</font> &amp; <span class="p1">(<span class="default"><font color="Maroon">u2</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">q</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">u1</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">q</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">u2</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">u1</font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">r</font> <a href="real_1.html#K4">*</a> <font color="Maroon">A2</font></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">w</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p0">(<span class="default"><font color="Maroon">r</font> <a href="real_1.html#K4">*</a> <font color="Maroon">A1</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">q</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">q</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">v1</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">q</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">r</font> <a href="real_1.html#K4">*</a> <font color="Maroon">A2</font></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">w</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p5">(<span class="default"><font color="Maroon">r</font> <a href="real_1.html#K4">*</a> <font color="Maroon">A1</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">q</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">v1</font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">r</font> <a href="real_1.html#K4">*</a> <font color="Maroon">B2</font></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">w</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p0">(<span class="default"><font color="Maroon">r</font> <a href="real_1.html#K4">*</a> <font color="Maroon">B1</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">q</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">q</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">v1</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">q</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">r</font> <a href="real_1.html#K4">*</a> <font color="Maroon">B2</font></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">w</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p5">(<span class="default"><font color="Maroon">r</font> <a href="real_1.html#K4">*</a> <font color="Maroon">B1</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">q</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">v1</font> )
 <b>by </b><i><a class="ref" href="euclmetr.html#D5" target="_self">Def5</a></i>;<br/><a NAME="E17:36_1_2"/><b>then </b>
( <font color="Maroon">u3</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">u1</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">r</font> <a href="real_1.html#K4">*</a> <font color="Maroon">A2</font></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">w</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p5">(<span class="default"><font color="Maroon">r</font> <a href="real_1.html#K4">*</a> <font color="Maroon">A1</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">q</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">v1</font> <a href="analmetr.html#R2">are_Ort_wrt</a> <font color="Maroon">w</font>,<font color="Maroon">y</font> &amp; <font color="Maroon">u2</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">u1</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">r</font> <a href="real_1.html#K4">*</a> <font color="Maroon">B2</font></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">w</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p5">(<span class="default"><font color="Maroon">r</font> <a href="real_1.html#K4">*</a> <font color="Maroon">B1</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">q</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">v1</font> <a href="analmetr.html#R2">are_Ort_wrt</a> <font color="Maroon">w</font>,<font color="Maroon">y</font> )
 <b>by </b><i>, , <a class="txt" href="euclmetr.html#E1:36_1"><i><font color="Green">E44</font></i></a>, </i>;<br/><a NAME="E18:36_1_2"/><b>then </b>
( <font color="Maroon">u1</font>,<font color="Maroon">u3</font>,<font color="Maroon">v1</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">r</font> <a href="real_1.html#K4">*</a> <font color="Maroon">A2</font></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">w</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p4">(<span class="default"><font color="Maroon">r</font> <a href="real_1.html#K4">*</a> <font color="Maroon">A1</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">q</font> <a href="analmetr.html#R3">are_Ort_wrt</a> <font color="Maroon">w</font>,<font color="Maroon">y</font> &amp; <font color="Maroon">u1</font>,<font color="Maroon">u2</font>,<font color="Maroon">v1</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">r</font> <a href="real_1.html#K4">*</a> <font color="Maroon">B2</font></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">w</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p4">(<span class="default"><font color="Maroon">r</font> <a href="real_1.html#K4">*</a> <font color="Maroon">B1</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">q</font> <a href="analmetr.html#R3">are_Ort_wrt</a> <font color="Maroon">w</font>,<font color="Maroon">y</font> )
 <b>by </b><i><a class="ref" href="analmetr.html#D3">ANALMETR:def 3</a></i>;<br/><a NAME="E19:36_1_2"/><b>then </b>
( <font color="Maroon">a</font>,<font color="Maroon">c</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">a1</font>,<font color="Maroon">c1'</font> &amp; <font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">a1</font>,<font color="Maroon">b1'</font> )
 <b>by </b><i><a class="txt" href="euclmetr.html#E1:36"><i><font color="Green">E34</font></i></a>, <a class="ref" href="analmetr.html#T31">ANALMETR:31</a></i>;<br/><a NAME="E20:36_1_2"/><b>then </b><i><font color="Green">E98</font></i>: 
( <font color="Maroon">c1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c1'</font> &amp; <font color="Maroon">b1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b1'</font> )
 <b>by </b><i><a class="txt" href="euclmetr.html#E2:36"><i><font color="Green">E35</font></i></a>, , , , , <a class="ref" href="euclmetr.html#D4" target="_self">Def4</a></i>;<br/><font color="Maroon">u3</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">u2</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">A1</font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">w</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p2">(<span class="default"><font color="Maroon">A2</font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">B1</font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">w</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p2">(<span class="default"><font color="Maroon">B2</font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">y</font></span>)</span></span>)</span>
<b>by </b><i>, <a class="txt" href="euclmetr.html#E1:36_1"><i><font color="Green">E44</font></i></a>, <a class="ref" href="euclmetr.html#D5" target="_self">Def5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">A1</font> <a href="real_1.html#K5">-</a> <font color="Maroon">B1</font></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">w</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">A2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">B2</font></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">y</font></span>)</span>
<b>by </b><i/>
;<br/><a NAME="E22:36_1_2"/><b>then </b><i><font color="Green">E99</font></i>: 
(  <a href="geomtrap.html#K2">pr1</a> <font color="Maroon">w</font>,<font color="Maroon">y</font>,<span class="p1">(<span class="default"><font color="Maroon">u3</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">u2</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">A1</font> <a href="real_1.html#K5">-</a> <font color="Maroon">B1</font> &amp;  <a href="geomtrap.html#K3">pr2</a> <font color="Maroon">w</font>,<font color="Maroon">y</font>,<span class="p1">(<span class="default"><font color="Maroon">u3</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">u2</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">A2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">B2</font> )
 <b>by </b><i><a class="ref" href="euclmetr.html#T1" target="_self">Th1</a>, <a class="ref" href="geomtrap.html#D4">GEOMTRAP:def 4</a>, <a class="ref" href="geomtrap.html#D5">GEOMTRAP:def 5</a></i>;<br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">r</font> <a href="real_1.html#K4">*</a> <font color="Maroon">A2</font></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">w</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p5">(<span class="default"><font color="Maroon">r</font> <a href="real_1.html#K4">*</a> <font color="Maroon">A1</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">q</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">r</font> <a href="real_1.html#K4">*</a> <font color="Maroon">B2</font></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">w</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p5">(<span class="default"><font color="Maroon">r</font> <a href="real_1.html#K4">*</a> <font color="Maroon">B1</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">q</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">r</font> <a href="real_1.html#K4">*</a> <font color="Maroon">A2</font></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">w</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">r</font> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default"><a href="real_1.html#K1">-</a> <font color="Maroon">A1</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">r</font> <a href="real_1.html#K4">*</a> <font color="Maroon">B2</font></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">w</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p4">(<span class="default"><font color="Maroon">r</font> <a href="real_1.html#K4">*</a> <font color="Maroon">B1</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">y</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="euclmetr.html#D5" target="_self">Def5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">r</font> <a href="real_1.html#K4">*</a> <font color="Maroon">A2</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Maroon">r</font> <a href="real_1.html#K4">*</a> <font color="Maroon">B2</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">w</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">r</font> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default"><a href="real_1.html#K1">-</a> <font color="Maroon">A1</font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Maroon">r</font> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default"><a href="real_1.html#K1">-</a> <font color="Maroon">B1</font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">y</font></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">r</font> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><font color="Maroon">A2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">B2</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">w</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">r</font> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><font color="Maroon">B1</font> <a href="real_1.html#K5">-</a> <font color="Maroon">A1</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">y</font></span>)</span>

;<br/><a NAME="E24:36_1_2"/><b>then </b>
(  <a href="geomtrap.html#K2">pr1</a> <font color="Maroon">w</font>,<font color="Maroon">y</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">r</font> <a href="real_1.html#K4">*</a> <font color="Maroon">A2</font></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">w</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p0">(<span class="default"><font color="Maroon">r</font> <a href="real_1.html#K4">*</a> <font color="Maroon">A1</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">q</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">r</font> <a href="real_1.html#K4">*</a> <font color="Maroon">B2</font></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">w</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p0">(<span class="default"><font color="Maroon">r</font> <a href="real_1.html#K4">*</a> <font color="Maroon">B1</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">q</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">r</font> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">A2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">B2</font></span>)</span> &amp;  <a href="geomtrap.html#K3">pr2</a> <font color="Maroon">w</font>,<font color="Maroon">y</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">r</font> <a href="real_1.html#K4">*</a> <font color="Maroon">A2</font></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">w</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p0">(<span class="default"><font color="Maroon">r</font> <a href="real_1.html#K4">*</a> <font color="Maroon">A1</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">q</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">r</font> <a href="real_1.html#K4">*</a> <font color="Maroon">B2</font></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">w</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p0">(<span class="default"><font color="Maroon">r</font> <a href="real_1.html#K4">*</a> <font color="Maroon">B1</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">q</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">r</font> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">B1</font> <a href="real_1.html#K5">-</a> <font color="Maroon">A1</font></span>)</span> )
 <b>by </b><i><a class="ref" href="euclmetr.html#T1" target="_self">Th1</a>, <a class="ref" href="geomtrap.html#D4">GEOMTRAP:def 4</a>, <a class="ref" href="geomtrap.html#D5">GEOMTRAP:def 5</a></i>;<br/><b>then </b> <a href="geomtrap.html#K4">PProJ</a> <font color="Maroon">w</font>,<font color="Maroon">y</font>,<span class="p1">(<span class="default"><font color="Maroon">u3</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">u2</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">r</font> <a href="real_1.html#K4">*</a> <font color="Maroon">A2</font></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">w</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p0">(<span class="default"><font color="Maroon">r</font> <a href="real_1.html#K4">*</a> <font color="Maroon">A1</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">q</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">r</font> <a href="real_1.html#K4">*</a> <font color="Maroon">B2</font></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">w</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p0">(<span class="default"><font color="Maroon">r</font> <a href="real_1.html#K4">*</a> <font color="Maroon">B1</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">q</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">A1</font> <a href="real_1.html#K5">-</a> <font color="Maroon">B1</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><font color="Maroon">r</font> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><font color="Maroon">A2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">B2</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">A2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">B2</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><font color="Maroon">r</font> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><font color="Maroon">B1</font> <a href="real_1.html#K5">-</a> <font color="Maroon">A1</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="euclmetr.html#E2:36_1"><i><font color="Green">E48</font></i></a>, <a class="ref" href="geomtrap.html#D6">GEOMTRAP:def 6</a></i>
<br/>.= 
0

;<br/><a NAME="E26:36_1_2"/><b>then </b>
<font color="Maroon">u3</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">u2</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">r</font> <a href="real_1.html#K4">*</a> <font color="Maroon">A2</font></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">w</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p5">(<span class="default"><font color="Maroon">r</font> <a href="real_1.html#K4">*</a> <font color="Maroon">A1</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">q</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">r</font> <a href="real_1.html#K4">*</a> <font color="Maroon">B2</font></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">w</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p5">(<span class="default"><font color="Maroon">r</font> <a href="real_1.html#K4">*</a> <font color="Maroon">B1</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">q</font></span>)</span> <a href="analmetr.html#R2">are_Ort_wrt</a> <font color="Maroon">w</font>,<font color="Maroon">y</font>
 <b>by </b><i><a class="ref" href="euclmetr.html#T1" target="_self">Th1</a>, <a class="ref" href="geomtrap.html#T34">GEOMTRAP:34</a></i>;<br/><a NAME="E27:36_1_2"/><b>then </b>
<font color="Maroon">u2</font>,<font color="Maroon">u3</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">r</font> <a href="real_1.html#K4">*</a> <font color="Maroon">B2</font></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">w</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p4">(<span class="default"><font color="Maroon">r</font> <a href="real_1.html#K4">*</a> <font color="Maroon">B1</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">q</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">r</font> <a href="real_1.html#K4">*</a> <font color="Maroon">A2</font></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">w</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p4">(<span class="default"><font color="Maroon">r</font> <a href="real_1.html#K4">*</a> <font color="Maroon">A1</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">q</font> <a href="analmetr.html#R3">are_Ort_wrt</a> <font color="Maroon">w</font>,<font color="Maroon">y</font>
 <b>by </b><i><a class="ref" href="analmetr.html#D3">ANALMETR:def 3</a></i>;<br/><b>hence </b><a NAME="E28:36_1_2"/>
<font color="Maroon">b</font>,<font color="Maroon">c</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">b1</font>,<font color="Maroon">c1</font>
 <b>by </b><i><a class="txt" href="euclmetr.html#E1:36"><i><font color="Green">E34</font></i></a>, , <a class="ref" href="analmetr.html#T31">ANALMETR:31</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E8:36_1"/>
<font color="Maroon">b</font>,<font color="Maroon">c</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">b1</font>,<font color="Maroon">c1</font>
 <b>by </b><i><a class="txt" href="euclmetr.html#E2:36"><i><font color="Green">E35</font></i></a>, , , </i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:36"/>
<font color="Maroon">MS</font> is <a href="euclmetr.html#V7" target="_self">Homogeneous</a>
 <b>by </b><i/>;<br/>


</div>
