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

<b>let </b><font color="Maroon" title="c4">F</font> be   <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Field</a>;<br/><b>let </b><font color="Maroon" title="c5">S</font> be   <a href="symsp_1.html#NM1" title="SYMSP_1:NM.1">SymSp</a> of <font color="Maroon" title="c4">F</font>;<br/><b>let </b><font color="Maroon" title="c6">a</font>, <font color="Maroon" title="c7">p</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>set </b><font color="Maroon" title="c10">0F</font> =  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c4">F</font>;<br/>
<b>set </b><font color="Maroon" title="c11">1F</font> =  <a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <font color="Maroon" title="c4">F</font>;<br/>
<b>assume </b><a NAME="E1:44"/><i><font color="Green" title="E39">A1</font></i>: 
( not <font color="Maroon" title="c6">a</font> <a href="symsp_1.html#R1" title="SYMSP_1:pred.1">_|_</a> <font color="Maroon" title="c7">p</font> &amp; not <font color="Maroon" title="c8">x</font> <a href="symsp_1.html#R1" title="SYMSP_1:pred.1">_|_</a> <font color="Maroon" title="c7">p</font> &amp; not <font color="Maroon" title="c9">y</font> <a href="symsp_1.html#R1" title="SYMSP_1:pred.1">_|_</a> <font color="Maroon" title="c7">p</font> )
 ;<br/>

<a NAME="E2:44"/><b>then </b><i><font color="Green" title="E40">A2</font></i>: 
( not <font color="Maroon" title="c6">a</font> <a href="symsp_1.html#R1" title="SYMSP_1:pred.1">_|_</a> <font color="Maroon" title="c7">p</font> &amp; not <font color="Maroon" title="c8">x</font> <a href="symsp_1.html#R1" title="SYMSP_1:pred.1">_|_</a> <font color="Maroon" title="c7">p</font> &amp; not <font color="Maroon" title="c9">y</font> <a href="symsp_1.html#R1" title="SYMSP_1:pred.1">_|_</a> <font color="Maroon" title="c7">p</font> &amp; not <font color="Maroon" title="c7">p</font> <a href="symsp_1.html#R1" title="SYMSP_1:pred.1">_|_</a> <font color="Maroon" title="c6">a</font> &amp; not <font color="Maroon" title="c7">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="Maroon" title="c7">p</font> <a href="symsp_1.html#R1" title="SYMSP_1:pred.1">_|_</a> <font color="Maroon" title="c9">y</font> )
 
<b>by </b><i><a class="ref" href="symsp_1.html#T12" target="_self" title="SYMSP_1:th.12">Th12</a></i>;<br/>
<div><i><font color="Green" title="E41">A3</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="44_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:44_1"/>
<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>
 ;<br/><a NAME="E2:44_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> &amp; <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> )
 <b>by </b><i><a class="ref" href="symsp_1.html#T12" target="_self" title="SYMSP_1:th.12">Th12</a></i>;<br/><a NAME="E3:44_1"/><b>then </b>
(  <a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c8">x</font>,<font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c9">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c4">F</font> &amp;  <a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c9">y</font>,<font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c4">F</font> )
 <b>by </b><i><a class="txt" href="symsp_1.html#E2:44"><i><font color="Green" title="E40">A2</font></i></a>, <a class="ref" href="symsp_1.html#T36" target="_self" title="SYMSP_1:th.36">Th36</a></i>;<br/><a NAME="E4:44_1"/><b>then </b>
( <span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">x</font></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c8">x</font>,<font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c9">y</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c4">F</font> &amp; <span class="p1">(<span class="default"><a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p2">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c6">a</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"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c9">y</font>,<font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c8">x</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c4">F</font> )
 <b>by </b><i><a class="ref" href="vectsp_1.html#T39" title="VECTSP_1:th.39">VECTSP_1:39</a></i>;<br/><b>hence </b><a NAME="E5:44_1"/>
<span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">x</font></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c8">x</font>,<font color="Maroon" title="c7">p</font>,<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"><a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p2">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c6">a</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"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c9">y</font>,<font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c8">x</font></span>)</span>
 ;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="44_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:44_2"/><i><font color="Green" title="E42">A4</font></i>: 
not <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>
 ;<br/><a NAME="E2:44_2"/><b>then </b><i><font color="Green" title="E43">A5</font></i>: 
( not <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; 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> )
 <b>by </b><i><a class="ref" href="symsp_1.html#T12" target="_self" title="SYMSP_1:th.12">Th12</a></i>;<br/><a NAME="E3:44_2"/>
<span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c9">y</font></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="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">x</font></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">"</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c8">x</font>,<font color="Maroon" title="c9">y</font>
 <b>by </b><i><a class="txt" href="symsp_1.html#E1:44"><i><font color="Green" title="E39">A1</font></i></a>, <a class="ref" href="symsp_1.html#T37" target="_self" title="SYMSP_1:th.37">Th37</a></i>;<br/><a NAME="E4:44_2"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c9">y</font></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">x</font></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">"</a> </span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">x</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="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c8">x</font>,<font color="Maroon" title="c9">y</font>,<font color="Maroon" title="c7">p</font></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">"</a> </span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p2">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c9">y</font>,<font color="Maroon" title="c8">x</font>,<font color="Maroon" title="c7">p</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="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">x</font></span>)</span>
 <b>by </b><i><a class="txt" href="symsp_1.html#E2:44"><i><font color="Green" title="E40">A2</font></i></a>, <a class="txt" href="symsp_1.html#E1:44_2"><i><font color="Green" title="E42">A4</font></i></a>, <a class="ref" href="symsp_1.html#T40" target="_self" title="SYMSP_1:th.40">Th40</a></i>;<br/><a NAME="E5:44_2"/><b>then </b><i><font color="Green" title="E44">A6</font></i>: 
<span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c9">y</font></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"><span class="p3">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">x</font></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">"</a> </span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p2">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">x</font></span>)</span></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="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c8">x</font>,<font color="Maroon" title="c9">y</font>,<font color="Maroon" title="c7">p</font></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">"</a> </span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p2">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c9">y</font>,<font color="Maroon" title="c8">x</font>,<font color="Maroon" title="c7">p</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="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">x</font></span>)</span>
 <b>by </b><i><a class="ref" href="group_1.html#D4" title="GROUP_1:def.4">GROUP_1:def 4</a></i>;<br/><a NAME="E6:44_2"/>
 <a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c4">F</font>
 <b>by </b><i><a class="txt" href="symsp_1.html#E1:44"><i><font color="Green" title="E39">A1</font></i></a>, <a class="ref" href="symsp_1.html#T36" target="_self" title="SYMSP_1:th.36">Th36</a></i>;<br/><a NAME="E7:44_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c9">y</font></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p1">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <font color="Maroon" title="c4">F</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="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c8">x</font>,<font color="Maroon" title="c9">y</font>,<font color="Maroon" title="c7">p</font></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">"</a> </span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p2">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c9">y</font>,<font color="Maroon" title="c8">x</font>,<font color="Maroon" title="c7">p</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="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">x</font></span>)</span>
 <b>by </b><i><a class="txt" href="symsp_1.html#E5:44_2"><i><font color="Green" title="E44">A6</font></i></a>, <a class="ref" href="vectsp_1.html#D22" title="VECTSP_1:def.22">VECTSP_1:def 22</a></i>;<br/><a NAME="E8:44_2"/><b>then </b>
 <a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c6">a</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="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c9">y</font>,<font color="Maroon" title="c8">x</font>,<font color="Maroon" title="c7">p</font></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p2">(<span class="default"><a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c8">x</font>,<font color="Maroon" title="c9">y</font>,<font color="Maroon" title="c7">p</font></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">"</a> </span>)</span></span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">x</font></span>)</span>
 <b>by </b><i><a class="ref" href="vectsp_1.html#D19" title="VECTSP_1:def.19">VECTSP_1:def 19</a></i>;<br/><a NAME="E9:44_2"/><b>then </b>
 <a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c9">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c9">y</font>,<font color="Maroon" title="c8">x</font>,<font color="Maroon" title="c7">p</font></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="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c8">x</font>,<font color="Maroon" title="c9">y</font>,<font color="Maroon" title="c7">p</font></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">"</a> </span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p2">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">x</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="group_1.html#D4" title="GROUP_1:def.4">GROUP_1:def 4</a></i>;<br/><a NAME="E10:44_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c9">y</font>,<font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c8">x</font></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c6">a</font>,<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"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c9">y</font>,<font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c8">x</font></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"><span class="p3">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c9">y</font>,<font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c8">x</font></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">"</a> </span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c8">x</font>,<font color="Maroon" title="c9">y</font>,<font color="Maroon" title="c7">p</font></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">"</a> </span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p3">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">x</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="symsp_1.html#E2:44"><i><font color="Green" title="E40">A2</font></i></a>, <a class="txt" href="symsp_1.html#E2:44_2"><i><font color="Green" title="E43">A5</font></i></a>, <a class="ref" href="symsp_1.html#T38" target="_self" title="SYMSP_1:th.38">Th38</a></i>;<br/><a NAME="E11:44_2"/><b>then </b><i><font color="Green" title="E45">A7</font></i>: 
<span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c9">y</font>,<font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c8">x</font></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c6">a</font>,<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="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c9">y</font>,<font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c8">x</font></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c9">y</font>,<font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c8">x</font></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">"</a> </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="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c8">x</font>,<font color="Maroon" title="c9">y</font>,<font color="Maroon" title="c7">p</font></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">"</a> </span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p2">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">x</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="group_1.html#D4" title="GROUP_1:def.4">GROUP_1:def 4</a></i>;<br/><a NAME="E12:44_2"/>
 <a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c9">y</font>,<font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c8">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c4">F</font>
 <b>by </b><i><a class="txt" href="symsp_1.html#E2:44"><i><font color="Green" title="E40">A2</font></i></a>, <a class="txt" href="symsp_1.html#E2:44_2"><i><font color="Green" title="E43">A5</font></i></a>, <a class="ref" href="symsp_1.html#T36" target="_self" title="SYMSP_1:th.36">Th36</a></i>;<br/><a NAME="E13:44_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c9">y</font>,<font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c8">x</font></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c6">a</font>,<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="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c8">x</font>,<font color="Maroon" title="c9">y</font>,<font color="Maroon" title="c7">p</font></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">"</a> </span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p2">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c6">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="group_1.html#K2" title="GROUP_1:func.2">1_</a> <font color="Maroon" title="c4">F</font></span>)</span>
 <b>by </b><i><a class="txt" href="symsp_1.html#E11:44_2"><i><font color="Green" title="E45">A7</font></i></a>, <a class="ref" href="vectsp_1.html#D22" title="VECTSP_1:def.22">VECTSP_1:def 22</a></i>;<br/><a NAME="E14:44_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c9">y</font></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c9">y</font>,<font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c8">x</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c8">x</font>,<font color="Maroon" title="c9">y</font>,<font color="Maroon" title="c7">p</font></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">"</a> </span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">x</font></span>)</span>
 <b>by </b><i><a class="ref" href="vectsp_1.html#D19" title="VECTSP_1:def.19">VECTSP_1:def 19</a></i>;<br/><a NAME="E15:44_2"/><b>then </b>
 <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c9">y</font></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p2">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c9">y</font>,<font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c8">x</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c8">x</font>,<font color="Maroon" title="c9">y</font>,<font color="Maroon" title="c7">p</font></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">"</a> </span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p3">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">x</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="vectsp_1.html#T41" title="VECTSP_1:th.41">VECTSP_1:41</a></i>;<br/><a NAME="E16:44_2"/><b>then </b>
 <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c9">y</font></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p2">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c9">y</font>,<font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c8">x</font></span>)</span></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="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c8">x</font>,<font color="Maroon" title="c9">y</font>,<font color="Maroon" title="c7">p</font></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">"</a> </span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">x</font></span>)</span>
 <b>by </b><i><a class="ref" href="rlvect_1.html#T30" title="RLVECT_1:th.30">RLVECT_1:30</a></i>;<br/><a NAME="E17:44_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p2">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c6">a</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"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c9">y</font>,<font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c8">x</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="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c8">x</font>,<font color="Maroon" title="c9">y</font>,<font color="Maroon" title="c7">p</font></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">"</a> </span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">x</font></span>)</span>
 <b>by </b><i><a class="ref" href="vectsp_1.html#T41" title="VECTSP_1:th.41">VECTSP_1:41</a></i>;<br/><b>hence </b><a NAME="E18:44_2"/>
<span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">x</font></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c8">x</font>,<font color="Maroon" title="c7">p</font>,<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"><a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p2">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c6">a</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"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c9">y</font>,<font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c8">x</font></span>)</span>
 <b>by </b><i><a class="txt" href="symsp_1.html#E2:44"><i><font color="Green" title="E40">A2</font></i></a>, <a class="txt" href="symsp_1.html#E1:44_2"><i><font color="Green" title="E42">A4</font></i></a>, <a class="ref" href="symsp_1.html#T38" target="_self" title="SYMSP_1:th.38">Th38</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:44"/>
<span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">x</font></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c8">x</font>,<font color="Maroon" title="c7">p</font>,<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"><a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p2">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c6">a</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"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c9">y</font>,<font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c8">x</font></span>)</span>
 <b>by </b><i><a class="txt" href="symsp_1.html#E3:44"><i><font color="Green" title="E41">A3</font></i></a></i>;<br/>


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