<?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> 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="c9">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>assume </b><a NAME="E1:28"/><i><font color="Green" title="E24">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/>

<b>set </b><font color="Maroon" title="c10">L</font> = <font color="Maroon" title="c8">x</font> <a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</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">a</font>,<font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c8">x</font></span>)</span> <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <font color="Maroon" title="c6">b</font></span>)</span>;<br/>
<a NAME="E2:28"/><i><font color="Green" title="E25">A2</font></i>: 
<font color="Maroon" title="c8">x</font> <a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</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">a</font>,<font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c8">x</font></span>)</span> <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <font color="Maroon" title="c6">b</font></span>)</span> <a href="symsp_1.html#R1" title="SYMSP_1:pred.1">_|_</a> <font color="Maroon" title="c7">a</font>
 
<b>by </b><i><a class="txt" href="symsp_1.html#E1:28"><i><font color="Green" title="E24">A1</font></i></a>, <a class="ref" href="symsp_1.html#T27" target="_self" title="SYMSP_1:th.27">Th27</a></i>;<br/>
<font color="Maroon" title="c9">l</font> <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">x</font> <a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</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">a</font>,<font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c8">x</font></span>)</span> <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <font color="Maroon" title="c6">b</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c9">l</font> <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <font color="Maroon" title="c8">x</font></span>)</span> <a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">l</font> <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</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">a</font>,<font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c8">x</font></span>)</span> <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <font color="Maroon" title="c6">b</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="vectsp_1.html#T70" title="VECTSP_1:th.70">VECTSP_1:70</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c9">l</font> <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <font color="Maroon" title="c8">x</font></span>)</span> <a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">l</font> <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">a</font>,<font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c8">x</font></span>)</span></span>)</span> <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <font color="Maroon" title="c6">b</font></span>)</span>
<b>by </b><i><a class="ref" href="vectsp_1.html#D26" title="VECTSP_1:def.26">VECTSP_1:def 26</a></i>
;<br/>
<a NAME="E4:28"/><b>then </b><i><font color="Green" title="E26">A3</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c9">l</font> <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <font color="Maroon" title="c8">x</font></span>)</span> <a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">l</font> <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">a</font>,<font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c8">x</font></span>)</span></span>)</span> <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <font color="Maroon" title="c6">b</font></span>)</span> <a href="symsp_1.html#R1" title="SYMSP_1:pred.1">_|_</a> <font color="Maroon" title="c7">a</font>
 
<b>by </b><i><a class="txt" href="symsp_1.html#E2:28"><i><font color="Green" title="E25">A2</font></i></a>, <a class="ref" href="symsp_1.html#D2" target="_self" title="SYMSP_1:def.2">Def2</a></i>;<br/>
<a NAME="E5:28"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c9">l</font> <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <font color="Maroon" title="c8">x</font></span>)</span> <a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</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">a</font>,<font color="Maroon" title="c6">b</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c9">l</font> <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <font color="Maroon" title="c8">x</font></span>)</span></span>)</span> <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <font color="Maroon" title="c6">b</font></span>)</span> <a href="symsp_1.html#R1" title="SYMSP_1:pred.1">_|_</a> <font color="Maroon" title="c7">a</font>
 
<b>by </b><i><a class="txt" href="symsp_1.html#E1:28"><i><font color="Green" title="E24">A1</font></i></a>, <a class="ref" href="symsp_1.html#T27" target="_self" title="SYMSP_1:th.27">Th27</a></i>;<br/>
<b>hence </b><a NAME="E6:28"/>
 <a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c6">b</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c9">l</font> <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <font color="Maroon" title="c8">x</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">l</font> <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">a</font>,<font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c8">x</font></span>)</span>
 <b>by </b><i><a class="txt" href="symsp_1.html#E1:28"><i><font color="Green" title="E24">A1</font></i></a>, <a class="txt" href="symsp_1.html#E4:28"><i><font color="Green" title="E26">A3</font></i></a>, <a class="ref" href="symsp_1.html#T24" target="_self" title="SYMSP_1:th.24">Th24</a></i>;<br/>


</div>
