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<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="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><b>that </b><br/><a NAME="E1:31"/><i><font color="Green" title="E26">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>
 <b>and </b><br/><a NAME="E2:31"/><i><font color="Green" title="E27">A2</font></i>: 
<font color="Maroon" title="c9">l</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="c4">F</font>
 ;<br/>

<a NAME="E3:31"/>
not <font color="Maroon" title="c6">b</font> <a href="symsp_1.html#R1" title="SYMSP_1:pred.1">_|_</a> <font color="Maroon" title="c9">l</font> <a href="vectsp_1.html#K6" title="VECTSP_1:func.6">*</a> <font color="Maroon" title="c7">a</font>
 
<b>by </b><i><a class="txt" href="symsp_1.html#E1:31"><i><font color="Green" title="E26">A1</font></i></a>, <a class="txt" href="symsp_1.html#E2:31"><i><font color="Green" title="E27">A2</font></i></a>, <a class="ref" href="symsp_1.html#T15" target="_self" title="SYMSP_1:th.15">Th15</a></i>;<br/>
<a NAME="E4:31"/><b>then </b><i><font color="Green" title="E28">A3</font></i>: 
( <font color="Maroon" title="c8">x</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</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#K6" title="VECTSP_1:func.6">*</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> &amp; <font color="Maroon" title="c8">x</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</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> <span class="p3">(<span class="default"><font color="Maroon" title="c9">l</font> <a href="vectsp_1.html#K6" title="VECTSP_1:func.6">*</a> <font color="Maroon" title="c7">a</font></span>)</span>,<font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c8">x</font></span>)</span> <a href="vectsp_1.html#K6" title="VECTSP_1:func.6">*</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="c9">l</font> <a href="vectsp_1.html#K6" title="VECTSP_1:func.6">*</a> <font color="Maroon" title="c7">a</font> )
 
<b>by </b><i><a class="txt" href="symsp_1.html#E1:31"><i><font color="Green" title="E26">A1</font></i></a>, <a class="ref" href="symsp_1.html#T27" target="_self" title="SYMSP_1:th.27">Th27</a></i>;<br/>
<a NAME="E5:31"/><b>then </b>
<font color="Maroon" title="c9">l</font> <a href="vectsp_1.html#K6" title="VECTSP_1:func.6">*</a> <font color="Maroon" title="c7">a</font> <a href="symsp_1.html#R1" title="SYMSP_1:pred.1">_|_</a> <font color="Maroon" title="c8">x</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</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> <span class="p3">(<span class="default"><font color="Maroon" title="c9">l</font> <a href="vectsp_1.html#K6" title="VECTSP_1:func.6">*</a> <font color="Maroon" title="c7">a</font></span>)</span>,<font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c8">x</font></span>)</span> <a href="vectsp_1.html#K6" title="VECTSP_1:func.6">*</a> <font color="Maroon" title="c6">b</font></span>)</span>
 
<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="E6:31"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c9">l</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">"</a> </span>)</span> <a href="vectsp_1.html#K6" title="VECTSP_1:func.6">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">l</font> <a href="vectsp_1.html#K6" title="VECTSP_1:func.6">*</a> <font color="Maroon" title="c7">a</font></span>)</span> <a href="symsp_1.html#R1" title="SYMSP_1:pred.1">_|_</a> <font color="Maroon" title="c8">x</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</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> <span class="p3">(<span class="default"><font color="Maroon" title="c9">l</font> <a href="vectsp_1.html#K6" title="VECTSP_1:func.6">*</a> <font color="Maroon" title="c7">a</font></span>)</span>,<font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c8">x</font></span>)</span> <a href="vectsp_1.html#K6" title="VECTSP_1:func.6">*</a> <font color="Maroon" title="c6">b</font></span>)</span>
 
<b>by </b><i><a class="ref" href="symsp_1.html#D2" target="_self" title="SYMSP_1:def.2">Def2</a></i>;<br/>
<a NAME="E7:31"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">l</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">"</a> </span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c9">l</font></span>)</span> <a href="vectsp_1.html#K6" title="VECTSP_1:func.6">*</a> <font color="Maroon" title="c7">a</font> <a href="symsp_1.html#R1" title="SYMSP_1:pred.1">_|_</a> <font color="Maroon" title="c8">x</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</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> <span class="p3">(<span class="default"><font color="Maroon" title="c9">l</font> <a href="vectsp_1.html#K6" title="VECTSP_1:func.6">*</a> <font color="Maroon" title="c7">a</font></span>)</span>,<font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c8">x</font></span>)</span> <a href="vectsp_1.html#K6" title="VECTSP_1:func.6">*</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="E8:31"/><b>then </b>
<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="vectsp_1.html#K6" title="VECTSP_1:func.6">*</a> <font color="Maroon" title="c7">a</font> <a href="symsp_1.html#R1" title="SYMSP_1:pred.1">_|_</a> <font color="Maroon" title="c8">x</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</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> <span class="p3">(<span class="default"><font color="Maroon" title="c9">l</font> <a href="vectsp_1.html#K6" title="VECTSP_1:func.6">*</a> <font color="Maroon" title="c7">a</font></span>)</span>,<font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c8">x</font></span>)</span> <a href="vectsp_1.html#K6" title="VECTSP_1:func.6">*</a> <font color="Maroon" title="c6">b</font></span>)</span>
 
<b>by </b><i><a class="txt" href="symsp_1.html#E2:31"><i><font color="Green" title="E27">A2</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="E9:31"/><b>then </b>
<font color="Maroon" title="c7">a</font> <a href="symsp_1.html#R1" title="SYMSP_1:pred.1">_|_</a> <font color="Maroon" title="c8">x</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</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> <span class="p3">(<span class="default"><font color="Maroon" title="c9">l</font> <a href="vectsp_1.html#K6" title="VECTSP_1:func.6">*</a> <font color="Maroon" title="c7">a</font></span>)</span>,<font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c8">x</font></span>)</span> <a href="vectsp_1.html#K6" title="VECTSP_1:func.6">*</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="E10:31"/><b>then </b>
<font color="Maroon" title="c8">x</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</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> <span class="p3">(<span class="default"><font color="Maroon" title="c9">l</font> <a href="vectsp_1.html#K6" title="VECTSP_1:func.6">*</a> <font color="Maroon" title="c7">a</font></span>)</span>,<font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c8">x</font></span>)</span> <a href="vectsp_1.html#K6" title="VECTSP_1:func.6">*</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="ref" href="symsp_1.html#T12" target="_self" title="SYMSP_1:th.12">Th12</a></i>;<br/>
<b>hence </b><a NAME="E11:31"/>
 <a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">l</font> <a href="vectsp_1.html#K6" title="VECTSP_1:func.6">*</a> <font color="Maroon" title="c7">a</font></span>)</span>,<font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c8">x</font> <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">a</font>,<font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c8">x</font>
 <b>by </b><i><a class="txt" href="symsp_1.html#E1:31"><i><font color="Green" title="E26">A1</font></i></a>, <a class="txt" href="symsp_1.html#E4:31"><i><font color="Green" title="E28">A3</font></i></a>, <a class="ref" href="symsp_1.html#T24" target="_self" title="SYMSP_1:th.24">Th24</a></i>;<br/>


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