<?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">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>assume </b><b>that </b><br/><a NAME="E1:46"/><i><font color="Green" title="E41">A1</font></i>: 
<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="rlvect_1.html#K3" title="RLVECT_1:func.3">+</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#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>and </b><br/><a NAME="E2:46"/><i><font color="Green" title="E42">A2</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> &amp; <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="c5">S</font> )
 ;<br/>

<a NAME="E3:46"/>
for <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>  holds <br/>( <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> or <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> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="46_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c10">p</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c5">S</font>;<br/>

<a NAME="E1:46_1"/>
<font color="Maroon" title="c8">x</font> <a href="symsp_1.html#R1" title="SYMSP_1:pred.1">_|_</a> <font color="Maroon" title="c10">p</font>
 
<b>by </b><i><a class="txt" href="symsp_1.html#E2:46"><i><font color="Green" title="E42">A2</font></i></a>, <a class="ref" href="symsp_1.html#T11" target="_self" title="SYMSP_1:th.11">Th11</a></i>;<br/>
<b>hence </b><a NAME="E2:46_1"/>
( <font color="Maroon" title="c10">p</font> <a href="symsp_1.html#R1" title="SYMSP_1:pred.1">_|_</a> <font color="Maroon" title="c7">a</font> or <font color="Maroon" title="c10">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="symsp_1.html#T12" target="_self" title="SYMSP_1:th.12">Th12</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:46"/>
 <a href="symsp_1.html#K2" title="SYMSP_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>  <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#E1:46"><i><font color="Green" title="E41">A1</font></i></a>, <a class="txt" href="symsp_1.html#E2:46"><i><font color="Green" title="E42">A2</font></i></a>, <a class="ref" href="symsp_1.html#D7" target="_self" title="SYMSP_1:def.7">Def7</a></i>;<br/>


</div>
