<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">F</font> be   <a href="vectsp_1.html#NM2">Field</a>;<br/><b>let </b><font color="Maroon">x</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">F</font>;<br/>



<b>assume </b><a NAME="E1:67"/><i><font color="Green">E46</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">F</font>
 ;<br/>

<b>assume </b><a NAME="E2:67"/><i><font color="Green">E53</font></i>: 
(  not <font color="Maroon">x</font> <a href="vectsp_1.html#K4" target="_self">"</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">F</font> or  not  <a href="rlvect_1.html#K5">-</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="vectsp_1.html#K4" target="_self">"</a> </span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">F</font> )
 ;<br/>

<div><i><font color="Green">E54</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="67_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:67_1"/>
<font color="Maroon">x</font> <a href="vectsp_1.html#K4" target="_self">"</a>  <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">F</font>
 ;<br/><a NAME="E2:67_1"/><b>then </b>
 <a href="group_1.html#K2">1.</a> <font color="Maroon">F</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">F</font></span>)</span>
 <b>by </b><i>, </i>;<br/><a NAME="E3:67_1"/><b>then </b>
 <a href="group_1.html#K2">1.</a> <font color="Maroon">F</font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">F</font>
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E4:67_1"/>
contradiction
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="67_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:67_2"/>
 <a href="rlvect_1.html#K5">-</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="vectsp_1.html#K4" target="_self">"</a> </span>)</span> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">F</font>
 ;<br/><a NAME="E2:67_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">F</font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="vectsp_1.html#K4" target="_self">"</a> </span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K5">-</a> <span class="p2">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">F</font></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">F</font></span>)</span>
 <b>by </b><i/>;<br/><a NAME="E3:67_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">F</font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="vectsp_1.html#K4" target="_self">"</a> </span>)</span> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">F</font>
 <b>by </b><i/>;<br/><a NAME="E4:67_2"/><b>then </b>
<font color="Maroon">x</font> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="vectsp_1.html#K4" target="_self">"</a> </span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">F</font></span>)</span>
 <b>by </b><i/>;<br/><a NAME="E5:67_2"/><b>then </b>
 <a href="group_1.html#K2">1.</a> <font color="Maroon">F</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">F</font></span>)</span>
 <b>by </b><i>, </i>;<br/><a NAME="E6:67_2"/><b>then </b>
 <a href="group_1.html#K2">1.</a> <font color="Maroon">F</font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">F</font>
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E7:67_2"/>
contradiction
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:67"/>
contradiction
 <b>by </b><i>, </i>;<br/>


</div>
