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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="ortsp_1.html#NM1" title="ORTSP_1:NM.1">OrtSp</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="group_1.html#K2" title="GROUP_1:func.2">1.</a> <font color="Maroon" title="c4">F</font>;<br/>
<b>assume </b><a NAME="E1:12"/><i><font color="Green" title="E12">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> &amp; not <font color="Maroon" title="c8">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <font color="Maroon" title="c4">F</font> )
 ;<br/>

<div><i><font color="Green" title="E13">A2</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="12_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:12_1"/><i><font color="Green" title="E14">A3</font></i>: 
<font color="Maroon" title="c8">l</font> <a href="vectsp_1.html#K6" title="VECTSP_1:func.6">*</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="E3:12_1"/><i><font color="Green" title="E15">A4</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="group_1.html#K2" title="GROUP_1:func.2">1.</a> <font color="Maroon" title="c4">F</font>
 <b>by </b><i><a class="txt" href="ortsp_1.html#E1:12"><i><font color="Green" title="E12">A1</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="E4:12_1"/>
<font color="Maroon" title="c10">k</font> <a href="vectsp_1.html#K6" title="VECTSP_1:func.6">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">l</font> <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="txt" href="ortsp_1.html#E1:12_1"><i><font color="Green" title="E14">A3</font></i></a>, <a class="ref" href="ortsp_1.html#D2" target="_self" title="ORTSP_1:def.2">Def2</a></i>;<br/><a NAME="E5:12_1"/><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="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="ortsp_1.html#E3:12_1"><i><font color="Green" title="E15">A4</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="E6:12_1"/>
contradiction
 <b>by </b><i><a class="txt" href="ortsp_1.html#E1:12"><i><font color="Green" title="E12">A1</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="12_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:12_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#K6" title="VECTSP_1:func.6">*</a> <font color="Maroon" title="c7">a</font>
 ;<br/><a NAME="E2:12_2"/><b>then </b><i><font color="Green" title="E14">A5</font></i>: 
<font color="Maroon" title="c8">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="c6">b</font>
 <b>by </b><i><a class="ref" href="ortsp_1.html#T12" target="_self" title="ORTSP_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="E4:12_2"/><i><font color="Green" title="E15">A6</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="group_1.html#K2" title="GROUP_1:func.2">1.</a> <font color="Maroon" title="c4">F</font>
 <b>by </b><i><a class="txt" href="ortsp_1.html#E1:12"><i><font color="Green" title="E12">A1</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="E5:12_2"/>
<font color="Maroon" title="c10">k</font> <a href="vectsp_1.html#K6" title="VECTSP_1:func.6">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">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="c6">b</font>
 <b>by </b><i><a class="txt" href="ortsp_1.html#E2:12_2"><i><font color="Green" title="E14">A5</font></i></a>, <a class="ref" href="ortsp_1.html#D2" target="_self" title="ORTSP_1:def.2">Def2</a></i>;<br/><a NAME="E6:12_2"/><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="c6">b</font>
 <b>by </b><i><a class="txt" href="ortsp_1.html#E4:12_2"><i><font color="Green" title="E15">A6</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="E7:12_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="ref" href="vectsp_1.html#D26" title="VECTSP_1:def.26">VECTSP_1:def 26</a></i>;<br/><b>hence </b><a NAME="E8:12_2"/>
contradiction
 <b>by </b><i><a class="txt" href="ortsp_1.html#E1:12"><i><font color="Green" title="E12">A1</font></i></a>, <a class="ref" href="ortsp_1.html#T12" target="_self" title="ORTSP_1:th.12">Th12</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:12"/>
( not <font color="Maroon" title="c8">l</font> <a href="vectsp_1.html#K6" title="VECTSP_1:func.6">*</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#K6" title="VECTSP_1:func.6">*</a> <font color="Maroon" title="c7">a</font> )
 <b>by </b><i><a class="txt" href="ortsp_1.html#E2:12"><i><font color="Green" title="E13">A2</font></i></a></i>;<br/>


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