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<b>let </b><font color="Maroon" title="c2">F</font> be   <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Field</a>;<br/><b>let </b><font color="Maroon" title="c3">x</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">F</font>;<br/>



<b>assume </b><a NAME="E1:80"/><i><font color="Green" title="E30">A1</font></i>: 
<font color="Maroon" title="c3">x</font> <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="c2">F</font>
 ;<br/>

<b>assume </b><a NAME="E2:80"/><i><font color="Green" title="E31">A2</font></i>: 
(  not <font color="Maroon" title="c3">x</font> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">"</a>  <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="c2">F</font> or  not  <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">"</a> </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="c2">F</font> )
 ;<br/>

<div><i><font color="Green" title="E32">A3</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="80_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:80_1"/><i><font color="Green" title="E33">A4</font></i>: 
<font color="Maroon" title="c3">x</font> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">"</a>  <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="c2">F</font>
 ;<br/> <a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <font color="Maroon" title="c2">F</font> = 
 <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c2">F</font>
<b>by </b><i><a class="txt" href="vectsp_1.html#E24"><i><font color="Green" title="E6">Lm2</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c3">x</font> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">F</font></span>)</span>
<b>by </b><i><a class="txt" href="vectsp_1.html#E1:80"><i><font color="Green" title="E30">A1</font></i></a>, <a class="txt" href="vectsp_1.html#E1:80_1"><i><font color="Green" title="E33">A4</font></i></a>, <a class="ref" href="vectsp_1.html#D22" target="_self" title="VECTSP_1:def.22">Def22</a></i>
;<br/><a NAME="E3:80_1"/><b>then </b>
 <a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <font color="Maroon" title="c2">F</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="c2">F</font>
 <b>by </b><i><a class="ref" href="vectsp_1.html#T39" target="_self" title="VECTSP_1:th.39">Th39</a></i>;<br/><b>hence </b><a NAME="E4:80_1"/>
contradiction
 <b>by </b><i><a class="ref" href="vectsp_1.html#D21" target="_self" title="VECTSP_1:def.21">Def21</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="80_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:80_2"/>
 <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">"</a> </span>)</span> <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="c2">F</font>
 ;<br/><a NAME="E2:80_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="c2">F</font></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">"</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p2">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <font color="Maroon" title="c2">F</font></span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">F</font></span>)</span>
 <b>by </b><i><a class="ref" href="vectsp_1.html#T42" target="_self" title="VECTSP_1:th.42">Th42</a></i>;<br/><a NAME="E3:80_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="c2">F</font></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">"</a> </span>)</span> <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="c2">F</font>
 <b>by </b><i><a class="ref" href="vectsp_1.html#T39" target="_self" title="VECTSP_1:th.39">Th39</a></i>;<br/><a NAME="E4:80_2"/><b>then </b>
<font color="Maroon" title="c3">x</font> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">"</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">x</font> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">F</font></span>)</span>
 <b>by </b><i><a class="ref" href="vectsp_1.html#D19" target="_self" title="VECTSP_1:def.19">Def19</a></i>;<br/><a NAME="E5:80_2"/><b>then </b>
 <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c2">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">x</font> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">F</font></span>)</span>
 <b>by </b><i><a class="txt" href="vectsp_1.html#E1:80"><i><font color="Green" title="E30">A1</font></i></a>, <a class="ref" href="vectsp_1.html#D22" target="_self" title="VECTSP_1:def.22">Def22</a></i>;<br/><a NAME="E6:80_2"/><b>then </b>
 <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c2">F</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="c2">F</font>
 <b>by </b><i><a class="ref" href="vectsp_1.html#T39" target="_self" title="VECTSP_1:th.39">Th39</a></i>;<br/><b>hence </b><a NAME="E7:80_2"/>
contradiction
 <b>by </b><i><a class="ref" href="struct_0.html#D8" title="STRUCT_0:def.8">STRUCT_0:def 8</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:80"/>
contradiction
 <b>by </b><i><a class="txt" href="vectsp_1.html#E2:80"><i><font color="Green" title="E31">A2</font></i></a>, <a class="txt" href="vectsp_1.html#E3:80"><i><font color="Green" title="E32">A3</font></i></a></i>;<br/>


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