<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">V</font> be   <a href="rlvect_1.html#NM2">RealLinearSpace</a>;<br/><b>let </b><font color="Maroon">p</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">V</font>;<br/><b>let </b><font color="Maroon">q</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">V</font>;<br/><b>let </b><font color="Maroon">u</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">V</font>;<br/><b>let </b><font color="Maroon">v</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">V</font>;<br/><b>let </b><font color="Maroon">a1</font> be   <a href="real_1.html#NM1">Real</a>;<br/><b>let </b><font color="Maroon">b1</font> be   <a href="real_1.html#NM1">Real</a>;<br/><b>let </b><font color="Maroon">a2</font> be   <a href="real_1.html#NM1">Real</a>;<br/><b>let </b><font color="Maroon">b2</font> be   <a href="real_1.html#NM1">Real</a>;<br/>

















<b>assume </b><a NAME="E1:18"/><i><font color="Green">E40</font></i>: 
( not  <a href="anproj_1.html#R1" target="_self">are_Prop</a> <font color="Maroon">p</font>,<font color="Maroon">q</font> &amp; <font color="Maroon">u</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">p</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">b1</font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">q</font></span>)</span> &amp; <font color="Maroon">v</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">a2</font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">p</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">q</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b2</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b1</font></span>)</span> <a href="hidden.html#R1">=</a> 0 &amp; <font color="Maroon">p</font> <a href="anproj_1.html#NR1" target="_self">is_Prop_Vect</a>  &amp; <font color="Maroon">q</font> <a href="anproj_1.html#NR1" target="_self">is_Prop_Vect</a>  )
 ;<br/>

<a NAME="E2:18"/><b>then </b><i><font color="Green">E41</font></i>: 
<font color="Maroon">a1</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b1</font>
 
;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="18_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:18_1"/>
( <font color="Maroon">u</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">v</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">V</font> )
 ;<br/><a NAME="E2:18_1"/><i><font color="Green">E42</font></i>: 
for <font color="Olive">p</font>, <font color="Olive">q</font>, <font color="Olive">u</font>, <font color="Olive">v</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">V</font><br/> for <font color="Olive">a1</font>, <font color="Olive">a2</font>, <font color="Olive">b1</font>, <font color="Olive">b2</font> being  <a href="real_1.html#NM1">Real</a>  st not  <a href="anproj_1.html#R1" target="_self">are_Prop</a> <font color="Olive">p</font>,<font color="Olive">q</font> &amp; <font color="Olive">u</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Olive">a1</font> <a href="rlvect_1.html#K3">*</a> <font color="Olive">p</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Olive">b1</font> <a href="rlvect_1.html#K3">*</a> <font color="Olive">q</font></span>)</span> &amp; <font color="Olive">v</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Olive">a2</font> <a href="rlvect_1.html#K3">*</a> <font color="Olive">p</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Olive">b2</font> <a href="rlvect_1.html#K3">*</a> <font color="Olive">q</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Olive">a1</font> <a href="real_1.html#K4">*</a> <font color="Olive">b2</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><font color="Olive">a2</font> <a href="real_1.html#K4">*</a> <font color="Olive">b1</font></span>)</span> <a href="hidden.html#R1">=</a> 0 &amp; <font color="Olive">p</font> <a href="anproj_1.html#NR1" target="_self">is_Prop_Vect</a>  &amp; <font color="Olive">q</font> <a href="anproj_1.html#NR1" target="_self">is_Prop_Vect</a>  &amp; <font color="Olive">a1</font> <a href="hidden.html#R1">=</a> 0 &amp; <font color="Olive">u</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="Olive">v</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">V</font> holds <br/> <a href="anproj_1.html#R1" target="_self">are_Prop</a> <font color="Olive">u</font>,<font color="Olive">v</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="18_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">p</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">V</font>;<br/><b>let </b><font color="Maroon">q</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">V</font>;<br/><b>let </b><font color="Maroon">u</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">V</font>;<br/><b>let </b><font color="Maroon">v</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">V</font>;<br/><b>let </b><font color="Maroon">a1</font> be   <a href="real_1.html#NM1">Real</a>;<br/><b>let </b><font color="Maroon">a2</font> be   <a href="real_1.html#NM1">Real</a>;<br/><b>let </b><font color="Maroon">b1</font> be   <a href="real_1.html#NM1">Real</a>;<br/><b>let </b><font color="Maroon">b2</font> be   <a href="real_1.html#NM1">Real</a>;<br/>















<b>assume </b><b>that </b><br/><a NAME="E1:18_1_1"/><i><font color="Green">E43</font></i>: 
( not  <a href="anproj_1.html#R1" target="_self">are_Prop</a> <font color="Maroon">p</font>,<font color="Maroon">q</font> &amp; <font color="Maroon">u</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">p</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">b1</font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">q</font></span>)</span> &amp; <font color="Maroon">v</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">a2</font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">p</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">q</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b2</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b1</font></span>)</span> <a href="hidden.html#R1">=</a> 0 &amp; <font color="Maroon">p</font> <a href="anproj_1.html#NR1" target="_self">is_Prop_Vect</a>  &amp; <font color="Maroon">q</font> <a href="anproj_1.html#NR1" target="_self">is_Prop_Vect</a>  )
 <b>and </b><br/><a NAME="E2:18_1_1"/><i><font color="Green">E45</font></i>: 
<font color="Maroon">a1</font> <a href="hidden.html#R1">=</a> 0
 <b>and </b><br/><a NAME="E3:18_1_1"/><i><font color="Green">E52</font></i>: 
( <font color="Maroon">u</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">v</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">V</font> )
 ;<br/>

<a NAME="E4:18_1_1"/>
0 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> <font color="Maroon">a2</font></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">b1</font>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E5:18_1_1"/><b>then </b><i><font color="Green">E53</font></i>: 
(  <a href="real_1.html#K1">-</a> <font color="Maroon">a2</font> <a href="hidden.html#R1">=</a> 0 or <font color="Maroon">b1</font> <a href="hidden.html#R1">=</a> 0 )
 
<b>by </b><i><a class="ref" href="xcmplx_1.html#T6">XCMPLX_1:6</a></i>;<br/>
<div><i><font color="Green">E58</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="18_1_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:18_1_1_1"/>
<font color="Maroon">b1</font> <a href="hidden.html#R1">=</a> 0
 ;<br/><b>then </b><font color="Maroon">u</font> = 
<span class="p1">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">V</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default">0 <a href="rlvect_1.html#K3">*</a> <font color="Maroon">q</font></span>)</span>
<b>by </b><i>, , <a class="ref" href="rlvect_1.html#T23">RLVECT_1:23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">V</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">V</font></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#T23">RLVECT_1:23</a></i>
;<br/><b>hence </b><a NAME="E3:18_1_1_1"/>
contradiction
 <b>by </b><i>, <a class="ref" href="rlvect_1.html#T10">RLVECT_1:10</a></i>;<br/></div><b>end;</b></div>
<a NAME="E7:18_1_1"/><b>then </b><i><font color="Green">E59</font></i>: 
( <font color="Maroon">a2</font> <a href="hidden.html#R1">=</a> 0 &amp; <font color="Maroon">b1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 )
 
<b>by </b><i/>;<br/>
<a NAME="E8:18_1_1"/><i><font color="Green">E60</font></i>: 
<font color="Maroon">b1</font> <a href="real_1.html#K2">"</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 
<b>by </b><i>, <a class="ref" href="xcmplx_1.html#T203">XCMPLX_1:203</a></i>;<br/>
<a NAME="E9:18_1_1"/>
( <font color="Maroon">u</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">V</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">b1</font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">q</font></span>)</span> &amp; <font color="Maroon">v</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">V</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">q</font></span>)</span> )
 
<b>by </b><i>, , , <a class="ref" href="rlvect_1.html#T23">RLVECT_1:23</a></i>;<br/>
<a NAME="E10:18_1_1"/><b>then </b>
( <font color="Maroon">u</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b1</font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">q</font> &amp; <font color="Maroon">v</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b2</font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">q</font> )
 
<b>by </b><i><a class="ref" href="rlvect_1.html#T10">RLVECT_1:10</a></i>;<br/>
<a NAME="E11:18_1_1"/><b>then </b>
<font color="Maroon">v</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b2</font> <a href="rlvect_1.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">b1</font> <a href="real_1.html#K2">"</a> </span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">u</font></span>)</span>
 
<b>by </b><i>, <a class="ref" href="analoaf.html#T12">ANALOAF:12</a></i>;<br/>
<a NAME="E12:18_1_1"/><b>then </b>
<font color="Maroon">v</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">b2</font> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><font color="Maroon">b1</font> <a href="real_1.html#K2">"</a> </span>)</span></span>)</span> <a href="rlvect_1.html#K3">*</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/>
<a NAME="E13:18_1_1"/><b>then </b><i><font color="Green">E61</font></i>: 
( 1 <a href="rlvect_1.html#K3">*</a> <font color="Maroon">v</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">b2</font> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><font color="Maroon">b1</font> <a href="real_1.html#K2">"</a> </span>)</span></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">u</font> &amp; 1 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 )
 
<b>by </b><i><a class="ref" href="rlvect_1.html#D9">RLVECT_1:def 9</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="18_1_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:18_1_1_2"/>
<font color="Maroon">b2</font> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">b1</font> <a href="real_1.html#K2">"</a> </span>)</span> <a href="hidden.html#R1">=</a> 0
 ;<br/><a NAME="E2:18_1_1_2"/><b>then </b>
<font color="Maroon">b2</font> <a href="hidden.html#R1">=</a> 0
 <b>by </b><i>, <a class="ref" href="xcmplx_1.html#T6">XCMPLX_1:6</a></i>;<br/><b>then </b><font color="Maroon">v</font> = 
<span class="p1">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">V</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default">0 <a href="rlvect_1.html#K3">*</a> <font color="Maroon">q</font></span>)</span>
<b>by </b><i>, , <a class="ref" href="rlvect_1.html#T23">RLVECT_1:23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">V</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">V</font></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#T23">RLVECT_1:23</a></i>
;<br/><b>hence </b><a NAME="E4:18_1_1_2"/>
contradiction
 <b>by </b><i>, <a class="ref" href="rlvect_1.html#T10">RLVECT_1:10</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E15:18_1_1"/>
 <a href="anproj_1.html#R1" target="_self">are_Prop</a> <font color="Maroon">u</font>,<font color="Maroon">v</font>
 <b>by </b><i>, </i>;<br/>


</div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="18_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:18_1_2"/><i><font color="Green">E62</font></i>: 
( <font color="Maroon">a1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 &amp; <font color="Maroon">a2</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 )
 ;<br/><div><i><font color="Green">E63</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="18_1_2_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:18_1_2_1"/><i><font color="Green">E69</font></i>: 
<font color="Maroon">b1</font> <a href="hidden.html#R1">=</a> 0
 ;<br/><a NAME="E2:18_1_2_1"/><b>then </b>
<font color="Maroon">b2</font> <a href="hidden.html#R1">=</a> 0
 <b>by </b><i>, , <a class="ref" href="xcmplx_1.html#T6">XCMPLX_1:6</a></i>;<br/><a NAME="E3:18_1_2_1"/><b>then </b>
( <font color="Maroon">u</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">p</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">V</font></span>)</span> &amp; <font color="Maroon">v</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">a2</font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">p</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">V</font></span>)</span> )
 <b>by </b><i>, , <a class="ref" href="rlvect_1.html#T23">RLVECT_1:23</a></i>;<br/><a NAME="E4:18_1_2_1"/><b>then </b><i><font color="Green">E70</font></i>: 
( <font color="Maroon">u</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a1</font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">p</font> &amp; <font color="Maroon">v</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a2</font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">p</font> &amp; <font color="Maroon">a1</font> <a href="real_1.html#K2">"</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 )
 <b>by </b><i>, <a class="ref" href="rlvect_1.html#T10">RLVECT_1:10</a>, <a class="ref" href="xcmplx_1.html#T203">XCMPLX_1:203</a></i>;<br/><b>then </b><font color="Maroon">v</font> = 
<font color="Maroon">a2</font> <a href="rlvect_1.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K2">"</a> </span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">u</font></span>)</span>
<b>by </b><i>, <a class="ref" href="analoaf.html#T12">ANALOAF:12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K2">"</a> </span>)</span></span>)</span> <a href="rlvect_1.html#K3">*</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/><a NAME="E6:18_1_2_1"/><b>then </b>
( 1 <a href="rlvect_1.html#K3">*</a> <font color="Maroon">v</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K2">"</a> </span>)</span></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">u</font> &amp; <font color="Maroon">a2</font> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K2">"</a> </span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 &amp; 1 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 )
 <b>by </b><i>, , <a class="ref" href="rlvect_1.html#D9">RLVECT_1:def 9</a>, <a class="ref" href="xcmplx_1.html#T6">XCMPLX_1:6</a></i>;<br/><b>hence </b><a NAME="E7:18_1_2_1"/>
 <a href="anproj_1.html#R1" target="_self">are_Prop</a> <font color="Maroon">u</font>,<font color="Maroon">v</font>
 <b>by </b><i/>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="18_1_2_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:18_1_2_2"/><i><font color="Green">E71</font></i>: 
<font color="Maroon">b1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 ;<br/><a NAME="E2:18_1_2_2"/><i><font color="Green">E72</font></i>: 
( <font color="Maroon">b2</font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">u</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a1</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">p</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">b2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b1</font></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">q</font></span>)</span> &amp; <font color="Maroon">b1</font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">v</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b1</font></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">p</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">b1</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">q</font></span>)</span> )
 <b>by </b><i>, </i>;<br/><a NAME="E3:18_1_2_2"/>
<font color="Maroon">b2</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 <b>by </b><i>, , , <a class="ref" href="xcmplx_1.html#T6">XCMPLX_1:6</a></i>;<br/><b>hence </b><a NAME="E4:18_1_2_2"/>
 <a href="anproj_1.html#R1" target="_self">are_Prop</a> <font color="Maroon">u</font>,<font color="Maroon">v</font>
 <b>by </b><i>, , , </i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E4:18_1_2"/>
(  <a href="anproj_1.html#R1" target="_self">are_Prop</a> <font color="Maroon">u</font>,<font color="Maroon">v</font> or <font color="Maroon">u</font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">V</font> or <font color="Maroon">v</font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">V</font> )
 <b>by </b><i/>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E4:18_1"/>
(  <a href="anproj_1.html#R1" target="_self">are_Prop</a> <font color="Maroon">u</font>,<font color="Maroon">v</font> or <font color="Maroon">u</font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">V</font> or <font color="Maroon">v</font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">V</font> )
 <b>by </b><i>, </i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:18"/>
(  <a href="anproj_1.html#R1" target="_self">are_Prop</a> <font color="Maroon">u</font>,<font color="Maroon">v</font> or <font color="Maroon">u</font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">V</font> or <font color="Maroon">v</font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">V</font> )
 ;<br/>


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