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

<b>let </b><font color="Maroon" title="c4">F</font> be   <a href="vectsp_1.html#NM2" title="VECTSP_1:NM.2">Field</a>;<br/><b>let </b><font color="Maroon" title="c5">S</font> be   <a href="ortsp_1.html#NM1" title="ORTSP_1:NM.1">OrtSp</a> of <font color="Maroon" title="c4">F</font>;<br/><b>let </b><font color="Maroon" title="c6">b</font>, <font color="Maroon" title="c7">a</font>, <font color="Maroon" title="c8">x</font>, <font color="Maroon" title="c9">y</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c5">S</font>;<br/><b>let </b><font color="Maroon" title="c10">l</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c4">F</font>;<br/>













<b>set </b><font color="Maroon" title="c11">0F</font> =  <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <font color="Maroon" title="c4">F</font>;<br/>
<b>assume </b><a NAME="E1:41"/><i><font color="Green" title="E35">A1</font></i>: 
not <font color="Maroon" title="c6">b</font> <a href="symsp_1.html#R1" title="SYMSP_1:pred.1">_|_</a> <font color="Maroon" title="c7">a</font>
 ;<br/>

<div><i><font color="Green" title="E36">A2</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="41_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:41_1"/><i><font color="Green" title="E37">A3</font></i>: 
<font color="Maroon" title="c8">x</font> <a href="symsp_1.html#R1" title="SYMSP_1:pred.1">_|_</a> <font color="Maroon" title="c9">y</font>
 ;<br/><a NAME="E2:41_1"/><b>then </b>
<font color="Maroon" title="c9">y</font> <a href="symsp_1.html#R1" title="SYMSP_1:pred.1">_|_</a> <font color="Maroon" title="c8">x</font>
 <b>by </b><i><a class="ref" href="ortsp_1.html#T12" target="_self" title="ORTSP_1:th.12">Th12</a></i>;<br/><a NAME="E3:41_1"/><b>then </b>
<font color="Maroon" title="c10">l</font> <a href="vectsp_1.html#K6" title="VECTSP_1:func.6">*</a> <font color="Maroon" title="c9">y</font> <a href="symsp_1.html#R1" title="SYMSP_1:pred.1">_|_</a> <font color="Maroon" title="c8">x</font>
 <b>by </b><i><a class="ref" href="ortsp_1.html#D2" target="_self" title="ORTSP_1:def.2">Def2</a></i>;<br/><a NAME="E4:41_1"/><b>then </b>
( <font color="Maroon" title="c8">x</font> <a href="symsp_1.html#R1" title="SYMSP_1:pred.1">_|_</a> <font color="Maroon" title="c9">y</font> &amp; <font color="Maroon" title="c9">y</font> <a href="symsp_1.html#R1" title="SYMSP_1:pred.1">_|_</a> <font color="Maroon" title="c8">x</font> &amp; <font color="Maroon" title="c10">l</font> <a href="vectsp_1.html#K6" title="VECTSP_1:func.6">*</a> <font color="Maroon" title="c9">y</font> <a href="symsp_1.html#R1" title="SYMSP_1:pred.1">_|_</a> <font color="Maroon" title="c8">x</font> &amp; <font color="Maroon" title="c8">x</font> <a href="symsp_1.html#R1" title="SYMSP_1:pred.1">_|_</a> <font color="Maroon" title="c10">l</font> <a href="vectsp_1.html#K6" title="VECTSP_1:func.6">*</a> <font color="Maroon" title="c9">y</font> )
 <b>by </b><i><a class="txt" href="ortsp_1.html#E1:41_1"><i><font color="Green" title="E37">A3</font></i></a>, <a class="ref" href="ortsp_1.html#T12" target="_self" title="ORTSP_1:th.12">Th12</a></i>;<br/><a NAME="E5:41_1"/><b>then </b>
( <font color="Maroon" title="c10">l</font> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p1">(<span class="default"><a href="ortsp_1.html#K2" title="ORTSP_1:func.2">PProJ</a> <font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c8">x</font>,<font color="Maroon" title="c9">y</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">l</font> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <font color="Maroon" title="c4">F</font></span>)</span> &amp;  <a href="ortsp_1.html#K2" title="ORTSP_1:func.2">PProJ</a> <font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c8">x</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c10">l</font> <a href="vectsp_1.html#K6" title="VECTSP_1:func.6">*</a> <font color="Maroon" title="c9">y</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <font color="Maroon" title="c4">F</font> )
 <b>by </b><i><a class="txt" href="ortsp_1.html#E1:41"><i><font color="Green" title="E35">A1</font></i></a>, <a class="ref" href="ortsp_1.html#T44" target="_self" title="ORTSP_1:th.44">Th44</a></i>;<br/><b>hence </b><a NAME="E6:41_1"/>
 <a href="ortsp_1.html#K2" title="ORTSP_1:func.2">PProJ</a> <font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c8">x</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c10">l</font> <a href="vectsp_1.html#K6" title="VECTSP_1:func.6">*</a> <font color="Maroon" title="c9">y</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">l</font> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p1">(<span class="default"><a href="ortsp_1.html#K2" title="ORTSP_1:func.2">PProJ</a> <font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c8">x</font>,<font color="Maroon" title="c9">y</font></span>)</span>
 <b>by </b><i><a class="ref" href="vectsp_1.html#T39" title="VECTSP_1:th.39">VECTSP_1:39</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="41_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:41_2"/>
not <font color="Maroon" title="c8">x</font> <a href="symsp_1.html#R1" title="SYMSP_1:pred.1">_|_</a> <font color="Maroon" title="c9">y</font>
 ;<br/><a NAME="E2:41_2"/><b>then </b>
( <font color="Maroon" title="c7">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <font color="Maroon" title="c5">S</font> &amp; <font color="Maroon" title="c8">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <font color="Maroon" title="c5">S</font> )
 <b>by </b><i><a class="txt" href="ortsp_1.html#E1:41"><i><font color="Green" title="E35">A1</font></i></a>, <a class="txt" href="ortsp_1.html#E59"><i><font color="Green" title="E33">Lm6</font></i></a>, <a class="ref" href="ortsp_1.html#T11" target="_self" title="ORTSP_1:th.11">Th11</a></i>;<br/><a NAME="E3:41_2"/><b>then </b>
 ex <font color="Olive" title="b1">p</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c5">S</font> st <br/>( not <font color="Olive" title="b1">p</font> <a href="symsp_1.html#R1" title="SYMSP_1:pred.1">_|_</a> <font color="Maroon" title="c7">a</font> &amp; not <font color="Olive" title="b1">p</font> <a href="symsp_1.html#R1" title="SYMSP_1:pred.1">_|_</a> <font color="Maroon" title="c8">x</font> &amp; not <font color="Olive" title="b1">p</font> <a href="symsp_1.html#R1" title="SYMSP_1:pred.1">_|_</a> <font color="Maroon" title="c7">a</font> &amp; not <font color="Olive" title="b1">p</font> <a href="symsp_1.html#R1" title="SYMSP_1:pred.1">_|_</a> <font color="Maroon" title="c8">x</font> )
 <b>by </b><i><a class="ref" href="ortsp_1.html#D2" target="_self" title="ORTSP_1:def.2">Def2</a></i>;<br/><b>then consider </b><font color="Maroon" title="c12">p</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c5">S</font><b> such that </b><br/><a NAME="E5:41_2"/><i><font color="Green" title="E37">A4</font></i>: 
( not <font color="Maroon" title="c12">p</font> <a href="symsp_1.html#R1" title="SYMSP_1:pred.1">_|_</a> <font color="Maroon" title="c7">a</font> &amp; not <font color="Maroon" title="c12">p</font> <a href="symsp_1.html#R1" title="SYMSP_1:pred.1">_|_</a> <font color="Maroon" title="c8">x</font> )
 ;<br/><a NAME="E6:41_2"/><i><font color="Green" title="E38">A5</font></i>: 
 <a href="ortsp_1.html#K2" title="ORTSP_1:func.2">PProJ</a> <font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c8">x</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c10">l</font> <a href="vectsp_1.html#K6" title="VECTSP_1:func.6">*</a> <font color="Maroon" title="c9">y</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c12">p</font></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p2">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c12">p</font>,<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">x</font></span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p1">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c8">x</font>,<font color="Maroon" title="c12">p</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c10">l</font> <a href="vectsp_1.html#K6" title="VECTSP_1:func.6">*</a> <font color="Maroon" title="c9">y</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="ortsp_1.html#E1:41"><i><font color="Green" title="E35">A1</font></i></a>, <a class="txt" href="ortsp_1.html#E5:41_2"><i><font color="Green" title="E37">A4</font></i></a>, <a class="ref" href="ortsp_1.html#D7" target="_self" title="ORTSP_1:def.7">Def7</a></i>;<br/><a NAME="E7:41_2"/><i><font color="Green" title="E39">A6</font></i>: 
 <a href="ortsp_1.html#K2" title="ORTSP_1:func.2">PProJ</a> <font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c8">x</font>,<font color="Maroon" title="c9">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c12">p</font></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p2">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c12">p</font>,<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">x</font></span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p1">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c8">x</font>,<font color="Maroon" title="c12">p</font>,<font color="Maroon" title="c9">y</font></span>)</span>
 <b>by </b><i><a class="txt" href="ortsp_1.html#E1:41"><i><font color="Green" title="E35">A1</font></i></a>, <a class="txt" href="ortsp_1.html#E5:41_2"><i><font color="Green" title="E37">A4</font></i></a>, <a class="ref" href="ortsp_1.html#D7" target="_self" title="ORTSP_1:def.7">Def7</a></i>;<br/><a NAME="E8:41_2"/>
 <a href="ortsp_1.html#K2" title="ORTSP_1:func.2">PProJ</a> <font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c8">x</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c10">l</font> <a href="vectsp_1.html#K6" title="VECTSP_1:func.6">*</a> <font color="Maroon" title="c9">y</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">l</font> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p2">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c8">x</font>,<font color="Maroon" title="c12">p</font>,<font color="Maroon" title="c9">y</font></span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c12">p</font></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p2">(<span class="default"><a href="ortsp_1.html#K1" title="ORTSP_1:func.1">ProJ</a> <font color="Maroon" title="c12">p</font>,<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">x</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="ortsp_1.html#E5:41_2"><i><font color="Green" title="E37">A4</font></i></a>, <a class="txt" href="ortsp_1.html#E6:41_2"><i><font color="Green" title="E38">A5</font></i></a>, <a class="ref" href="ortsp_1.html#T25" target="_self" title="ORTSP_1:th.25">Th25</a></i>;<br/><b>hence </b><a NAME="E9:41_2"/>
 <a href="ortsp_1.html#K2" title="ORTSP_1:func.2">PProJ</a> <font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c8">x</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c10">l</font> <a href="vectsp_1.html#K6" title="VECTSP_1:func.6">*</a> <font color="Maroon" title="c9">y</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">l</font> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p1">(<span class="default"><a href="ortsp_1.html#K2" title="ORTSP_1:func.2">PProJ</a> <font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c8">x</font>,<font color="Maroon" title="c9">y</font></span>)</span>
 <b>by </b><i><a class="txt" href="ortsp_1.html#E7:41_2"><i><font color="Green" title="E39">A6</font></i></a>, <a class="ref" href="group_1.html#D4" title="GROUP_1:def.4">GROUP_1:def 4</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:41"/>
 <a href="ortsp_1.html#K2" title="ORTSP_1:func.2">PProJ</a> <font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c8">x</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c10">l</font> <a href="vectsp_1.html#K6" title="VECTSP_1:func.6">*</a> <font color="Maroon" title="c9">y</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">l</font> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p1">(<span class="default"><a href="ortsp_1.html#K2" title="ORTSP_1:func.2">PProJ</a> <font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c8">x</font>,<font color="Maroon" title="c9">y</font></span>)</span>
 <b>by </b><i><a class="txt" href="ortsp_1.html#E2:41"><i><font color="Green" title="E36">A2</font></i></a></i>;<br/>


</div>
