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<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> 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="c8">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="c9">1F</font> =  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c4">F</font>;<br/>
<a NAME="E1:17"/><i><font color="Green" title="E13">A1</font></i>: 
 <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c4">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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="E2:17"/><i><font color="Green" title="E14">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; not <font color="Maroon" title="c8">l</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> )
 ;<br/>

<div><i><font color="Green" title="E15">A3</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="17_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:17_1"/><i><font color="Green" title="E16">A4</font></i>: 
<font color="Maroon" title="c8">l</font> <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <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>consider </b><font color="Maroon" title="c10">k</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c4">F</font><b> such that </b><br/><a NAME="E3:17_1"/><i><font color="Green" title="E17">A5</font></i>: 
<font color="Maroon" title="c8">l</font> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c10">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c4">F</font>
 <b>by </b><i><a class="txt" href="symsp_1.html#E2:17"><i><font color="Green" title="E14">A2</font></i></a>, <a class="ref" href="vectsp_1.html#D20" title="VECTSP_1:def.20">VECTSP_1:def 20</a></i>;<br/><a NAME="E4:17_1"/>
<font color="Maroon" title="c10">k</font> <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">l</font> <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#E1:17_1"><i><font color="Green" title="E16">A4</font></i></a>, <a class="ref" href="symsp_1.html#D2" target="_self" title="SYMSP_1:def.2">Def2</a></i>;<br/><a NAME="E5:17_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c4">F</font></span>)</span> <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <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>by </b><i><a class="txt" href="symsp_1.html#E3:17_1"><i><font color="Green" title="E17">A5</font></i></a>, <a class="ref" href="vectsp_1.html#D26" title="VECTSP_1:def.26">VECTSP_1:def 26</a></i>;<br/><b>hence </b><a NAME="E6:17_1"/>
contradiction
 <b>by </b><i><a class="txt" href="symsp_1.html#E1:17"><i><font color="Green" title="E13">A1</font></i></a>, <a class="txt" href="symsp_1.html#E2:17"><i><font color="Green" title="E14">A2</font></i></a>, <a class="ref" href="vectsp_1.html#D26" title="VECTSP_1:def.26">VECTSP_1:def 26</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:17_2"/>
<font color="Maroon" title="c6">b</font> <a href="symsp_1.html#R1" title="SYMSP_1:pred.1">_|_</a> <font color="Maroon" title="c8">l</font> <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <font color="Maroon" title="c7">a</font>
 ;<br/><a NAME="E2:17_2"/><b>then </b><i><font color="Green" title="E16">A6</font></i>: 
<font color="Maroon" title="c8">l</font> <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <font color="Maroon" title="c7">a</font> <a href="symsp_1.html#R1" title="SYMSP_1:pred.1">_|_</a> <font color="Maroon" title="c6">b</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>consider </b><font color="Maroon" title="c10">k</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c4">F</font><b> such that </b><br/><a NAME="E4:17_2"/><i><font color="Green" title="E17">A7</font></i>: 
<font color="Maroon" title="c8">l</font> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c10">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c4">F</font>
 <b>by </b><i><a class="txt" href="symsp_1.html#E2:17"><i><font color="Green" title="E14">A2</font></i></a>, <a class="ref" href="vectsp_1.html#D20" title="VECTSP_1:def.20">VECTSP_1:def 20</a></i>;<br/><a NAME="E5:17_2"/>
<font color="Maroon" title="c10">k</font> <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">l</font> <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</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="c6">b</font>
 <b>by </b><i><a class="txt" href="symsp_1.html#E2:17_2"><i><font color="Green" title="E16">A6</font></i></a>, <a class="ref" href="symsp_1.html#D2" target="_self" title="SYMSP_1:def.2">Def2</a></i>;<br/><a NAME="E6:17_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c4">F</font></span>)</span> <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <font color="Maroon" title="c7">a</font> <a href="symsp_1.html#R1" title="SYMSP_1:pred.1">_|_</a> <font color="Maroon" title="c6">b</font>
 <b>by </b><i><a class="txt" href="symsp_1.html#E4:17_2"><i><font color="Green" title="E17">A7</font></i></a>, <a class="ref" href="vectsp_1.html#D26" title="VECTSP_1:def.26">VECTSP_1:def 26</a></i>;<br/><a NAME="E7:17_2"/><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="c6">b</font>
 <b>by </b><i><a class="txt" href="symsp_1.html#E1:17"><i><font color="Green" title="E13">A1</font></i></a>, <a class="ref" href="vectsp_1.html#D26" title="VECTSP_1:def.26">VECTSP_1:def 26</a></i>;<br/><b>hence </b><a NAME="E8:17_2"/>
contradiction
 <b>by </b><i><a class="txt" href="symsp_1.html#E2:17"><i><font color="Green" title="E14">A2</font></i></a>, <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="E5:17"/>
( not <font color="Maroon" title="c8">l</font> <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <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; not <font color="Maroon" title="c6">b</font> <a href="symsp_1.html#R1" title="SYMSP_1:pred.1">_|_</a> <font color="Maroon" title="c8">l</font> <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <font color="Maroon" title="c7">a</font> )
 <b>by </b><i><a class="txt" href="symsp_1.html#E3:17"><i><font color="Green" title="E15">A3</font></i></a></i>;<br/>


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