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

<b>let </b><font color="Maroon">F</font> be   <a href="vectsp_1.html#NM2">Field</a>;<br/><b>let </b><font color="Maroon">S</font> be   <a href="ortsp_1.html#NM1">OrtSp</a> of <font color="Maroon">F</font>;<br/><b>let </b><font color="Maroon">p</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">S</font>;<br/><b>let </b><font color="Maroon">a</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">S</font>;<br/><b>let </b><font color="Maroon">x</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">S</font>;<br/><b>let </b><font color="Maroon">q</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">S</font>;<br/><b>let </b><font color="Maroon">b</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">S</font>;<br/><b>let </b><font color="Maroon">y</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">S</font>;<br/>















<b>set </b><font color="Maroon">0F</font> =  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">F</font>;<br/>
<b>set </b><font color="Maroon">1F</font> =  <a href="group_1.html#K2">1.</a> <font color="Maroon">F</font>;<br/>
<b>assume </b><a NAME="E1:34"/><i><font color="Green">E22</font></i>: 
( not <font color="Maroon">p</font> <a href="symsp_1.html#R1">_|_</a> <font color="Maroon">a</font> &amp; not <font color="Maroon">p</font> <a href="symsp_1.html#R1">_|_</a> <font color="Maroon">x</font> &amp; not <font color="Maroon">q</font> <a href="symsp_1.html#R1">_|_</a> <font color="Maroon">a</font> &amp; not <font color="Maroon">q</font> <a href="symsp_1.html#R1">_|_</a> <font color="Maroon">x</font> &amp; not <font color="Maroon">b</font> <a href="symsp_1.html#R1">_|_</a> <font color="Maroon">a</font> )
 ;<br/>

<div><i><font color="Green">E26</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="34_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:34_1"/>
<font color="Maroon">y</font> <a href="symsp_1.html#R1">_|_</a> <font color="Maroon">x</font>
 ;<br/><a NAME="E2:34_1"/><b>then </b>
(  <a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">x</font>,<font color="Maroon">p</font>,<font color="Maroon">y</font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">F</font> &amp;  <a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">x</font>,<font color="Maroon">q</font>,<font color="Maroon">y</font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">F</font> )
 <b>by </b><i>, <a class="txt" href="ortsp_1.html#E6"><i><font color="Green">Lemma23</font></i></a></i>;<br/><a NAME="E3:34_1"/><b>then </b>
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">p</font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">p</font>,<font color="Maroon">a</font>,<font color="Maroon">x</font></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">x</font>,<font color="Maroon">p</font>,<font color="Maroon">y</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">F</font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">q</font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">q</font>,<font color="Maroon">a</font>,<font color="Maroon">x</font></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">x</font>,<font color="Maroon">q</font>,<font color="Maroon">y</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">F</font> )
 <b>by </b><i><a class="ref" href="vectsp_1.html#T39">VECTSP_1:39</a></i>;<br/><b>hence </b><a NAME="E4:34_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">p</font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">p</font>,<font color="Maroon">a</font>,<font color="Maroon">x</font></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">x</font>,<font color="Maroon">p</font>,<font color="Maroon">y</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">q</font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">q</font>,<font color="Maroon">a</font>,<font color="Maroon">x</font></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">x</font>,<font color="Maroon">q</font>,<font color="Maroon">y</font></span>)</span>
 ;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="34_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:34_2"/><i><font color="Green">E27</font></i>: 
not <font color="Maroon">y</font> <a href="symsp_1.html#R1">_|_</a> <font color="Maroon">x</font>
 ;<br/><a NAME="E2:34_2"/>
<span class="p1">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">a</font>,<font color="Maroon">q</font>,<font color="Maroon">p</font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">p</font>,<font color="Maroon">a</font>,<font color="Maroon">x</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">x</font>,<font color="Maroon">q</font>,<font color="Maroon">p</font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">q</font>,<font color="Maroon">a</font>,<font color="Maroon">x</font></span>)</span>
 <b>by </b><i><a class="txt" href="ortsp_1.html#E14:34_2"><i><font color="Green">E30</font></i></a>, </i>;<br/><a NAME="E3:34_2"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">p</font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">q</font></span>)</span> <a href="vectsp_1.html#K4">"</a> </span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">p</font>,<font color="Maroon">a</font>,<font color="Maroon">x</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">x</font>,<font color="Maroon">q</font>,<font color="Maroon">p</font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">q</font>,<font color="Maroon">a</font>,<font color="Maroon">x</font></span>)</span>
 <b>by </b><i><a class="txt" href="ortsp_1.html#E14:34_2"><i><font color="Green">E30</font></i></a>, </i>;<br/><a NAME="E4:34_2"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">q</font></span>)</span> <a href="vectsp_1.html#K4">"</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">p</font></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">p</font>,<font color="Maroon">a</font>,<font color="Maroon">x</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">p</font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">q</font></span>)</span> <a href="vectsp_1.html#K4">"</a> </span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">q</font>,<font color="Maroon">a</font>,<font color="Maroon">x</font></span>)</span>
 <b>by </b><i><a class="txt" href="ortsp_1.html#E14:34_2"><i><font color="Green">E30</font></i></a>, , </i>;<br/><a NAME="E5:34_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">q</font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">q</font></span>)</span> <a href="vectsp_1.html#K4">"</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">p</font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p3">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">p</font>,<font color="Maroon">a</font>,<font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">q</font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">p</font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">q</font></span>)</span> <a href="vectsp_1.html#K4">"</a> </span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">q</font>,<font color="Maroon">a</font>,<font color="Maroon">x</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="group_1.html#D4">GROUP_1:def 4</a></i>;<br/><a NAME="E6:34_2"/><b>then </b><i><font color="Green">E29</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">q</font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">q</font></span>)</span> <a href="vectsp_1.html#K4">"</a> </span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">p</font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">p</font>,<font color="Maroon">a</font>,<font color="Maroon">x</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">q</font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">p</font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">q</font></span>)</span> <a href="vectsp_1.html#K4">"</a> </span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">q</font>,<font color="Maroon">a</font>,<font color="Maroon">x</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="group_1.html#D4">GROUP_1:def 4</a></i>;<br/><a NAME="E7:34_2"/>
 <a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<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">F</font>
 <b>by </b><i><a class="txt" href="ortsp_1.html#E14:34_2"><i><font color="Green">E30</font></i></a>, <a class="txt" href="ortsp_1.html#E6"><i><font color="Green">Lemma23</font></i></a></i>;<br/><a NAME="E8:34_2"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">p</font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">p</font>,<font color="Maroon">a</font>,<font color="Maroon">x</font></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">F</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">q</font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">p</font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">q</font></span>)</span> <a href="vectsp_1.html#K4">"</a> </span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">q</font>,<font color="Maroon">a</font>,<font color="Maroon">x</font></span>)</span></span>)</span>
 <b>by </b><i>, <a class="ref" href="vectsp_1.html#D22">VECTSP_1:def 22</a></i>;<br/><a NAME="E9:34_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">p</font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">p</font>,<font color="Maroon">a</font>,<font color="Maroon">x</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">q</font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">p</font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">q</font></span>)</span> <a href="vectsp_1.html#K4">"</a> </span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">q</font>,<font color="Maroon">a</font>,<font color="Maroon">x</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="vectsp_1.html#D19">VECTSP_1:def 19</a></i>;<br/><a NAME="E10:34_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">p</font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">p</font>,<font color="Maroon">a</font>,<font color="Maroon">x</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">q</font></span>)</span> <a href="group_1.html#K10">*</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"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">q</font></span>)</span> <a href="vectsp_1.html#K4">"</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">x</font>,<font color="Maroon">p</font>,<font color="Maroon">y</font></span>)</span> <a href="vectsp_1.html#K4">"</a> </span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">q</font>,<font color="Maroon">a</font>,<font color="Maroon">x</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="ortsp_1.html#E14:34_2"><i><font color="Green">E30</font></i></a>, , </i>;<br/><a NAME="E11:34_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">p</font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">p</font>,<font color="Maroon">a</font>,<font color="Maroon">x</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">q</font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">q</font></span>)</span> <a href="vectsp_1.html#K4">"</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">x</font>,<font color="Maroon">p</font>,<font color="Maroon">y</font></span>)</span> <a href="vectsp_1.html#K4">"</a> </span>)</span></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">q</font>,<font color="Maroon">a</font>,<font color="Maroon">x</font></span>)</span>
 <b>by </b><i><a class="ref" href="group_1.html#D4">GROUP_1:def 4</a></i>;<br/><a NAME="E12:34_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">p</font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">p</font>,<font color="Maroon">a</font>,<font color="Maroon">x</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">q</font>,<font color="Maroon">a</font>,<font color="Maroon">x</font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">q</font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">q</font></span>)</span> <a href="vectsp_1.html#K4">"</a> </span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">x</font>,<font color="Maroon">p</font>,<font color="Maroon">y</font></span>)</span> <a href="vectsp_1.html#K4">"</a> </span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="group_1.html#D4">GROUP_1:def 4</a></i>;<br/><a NAME="E13:34_2"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">p</font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">p</font>,<font color="Maroon">a</font>,<font color="Maroon">x</font></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">x</font>,<font color="Maroon">p</font>,<font color="Maroon">y</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"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">q</font>,<font color="Maroon">a</font>,<font color="Maroon">x</font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">q</font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">q</font></span>)</span> <a href="vectsp_1.html#K4">"</a> </span>)</span></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">x</font>,<font color="Maroon">p</font>,<font color="Maroon">y</font></span>)</span> <a href="vectsp_1.html#K4">"</a> </span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">x</font>,<font color="Maroon">p</font>,<font color="Maroon">y</font></span>)</span>
 <b>by </b><i><a class="ref" href="group_1.html#D4">GROUP_1:def 4</a></i>;<br/><a NAME="E14:34_2"/><b>then </b><i><font color="Green">E30</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">p</font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">p</font>,<font color="Maroon">a</font>,<font color="Maroon">x</font></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">x</font>,<font color="Maroon">p</font>,<font color="Maroon">y</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">q</font>,<font color="Maroon">a</font>,<font color="Maroon">x</font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">q</font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">q</font></span>)</span> <a href="vectsp_1.html#K4">"</a> </span>)</span></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">x</font>,<font color="Maroon">p</font>,<font color="Maroon">y</font></span>)</span> <a href="vectsp_1.html#K4">"</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">x</font>,<font color="Maroon">p</font>,<font color="Maroon">y</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="group_1.html#D4">GROUP_1:def 4</a></i>;<br/><a NAME="E15:34_2"/>
 <a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">x</font>,<font color="Maroon">p</font>,<font color="Maroon">y</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">F</font>
 <b>by </b><i><a class="txt" href="ortsp_1.html#E14:34_2"><i><font color="Green">E30</font></i></a>, , <a class="txt" href="ortsp_1.html#E6"><i><font color="Green">Lemma23</font></i></a></i>;<br/><a NAME="E16:34_2"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">p</font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">p</font>,<font color="Maroon">a</font>,<font color="Maroon">x</font></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">x</font>,<font color="Maroon">p</font>,<font color="Maroon">y</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">q</font>,<font color="Maroon">a</font>,<font color="Maroon">x</font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">q</font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">q</font></span>)</span> <a href="vectsp_1.html#K4">"</a> </span>)</span></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">F</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="vectsp_1.html#D22">VECTSP_1:def 22</a></i>;<br/><a NAME="E17:34_2"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">p</font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">p</font>,<font color="Maroon">a</font>,<font color="Maroon">x</font></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">x</font>,<font color="Maroon">p</font>,<font color="Maroon">y</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">q</font>,<font color="Maroon">a</font>,<font color="Maroon">x</font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">q</font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">q</font></span>)</span> <a href="vectsp_1.html#K4">"</a> </span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="vectsp_1.html#D19">VECTSP_1:def 19</a></i>;<br/><a NAME="E18:34_2"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">p</font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">p</font>,<font color="Maroon">a</font>,<font color="Maroon">x</font></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">x</font>,<font color="Maroon">p</font>,<font color="Maroon">y</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">q</font>,<font color="Maroon">a</font>,<font color="Maroon">x</font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">q</font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">x</font>,<font color="Maroon">q</font>,<font color="Maroon">y</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="ortsp_1.html#E14:34_2"><i><font color="Green">E30</font></i></a>, , </i>;<br/><b>hence </b><a NAME="E19:34_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">p</font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">p</font>,<font color="Maroon">a</font>,<font color="Maroon">x</font></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">x</font>,<font color="Maroon">p</font>,<font color="Maroon">y</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">q</font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">q</font>,<font color="Maroon">a</font>,<font color="Maroon">x</font></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">x</font>,<font color="Maroon">q</font>,<font color="Maroon">y</font></span>)</span>
 <b>by </b><i><a class="ref" href="group_1.html#D4">GROUP_1:def 4</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:34"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">p</font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">p</font>,<font color="Maroon">a</font>,<font color="Maroon">x</font></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">x</font>,<font color="Maroon">p</font>,<font color="Maroon">y</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">q</font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">q</font>,<font color="Maroon">a</font>,<font color="Maroon">x</font></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">x</font>,<font color="Maroon">q</font>,<font color="Maroon">y</font></span>)</span>
 <b>by </b><i/>;<br/>


</div>
