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<b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="vectsp_1.html#NM2">Field</a>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>



<b>assume </b><a NAME="E1:67"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<b>assume </b><a NAME="E2:67"/><i><font color="Green">E29</font></i>: 
(  not <font color="Maroon">c<sub>3</sub></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">c<sub>2</sub></font> or  not  <a href="rlvect_1.html#K5">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></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">c<sub>2</sub></font> )
 ;<br/>

<div><i><font color="Green">E30</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">c<sub>3</sub></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">c<sub>2</sub></font>
 ;<br/><a NAME="E2:67_1"/><b>then </b>
 <a href="group_1.html#K2">1.</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></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">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="vectsp_1.html#E1:67"><i><font color="Green">E28</font></i></a>, <a class="ref" href="vectsp_1.html#D22" target="_self">Def22</a></i>;<br/><a NAME="E3:67_1"/><b>then </b>
 <a href="group_1.html#K2">1.</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="vectsp_1.html#T39" target="_self">Th39</a></i>;<br/><b>hence </b><a NAME="E4:67_1"/>
contradiction
 <b>by </b><i><a class="ref" href="vectsp_1.html#D21" target="_self">Def21</a></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">c<sub>3</sub></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">c<sub>2</sub></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">c<sub>2</sub></font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></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">c<sub>2</sub></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">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="vectsp_1.html#T42" target="_self">Th42</a></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">c<sub>2</sub></font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></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">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="vectsp_1.html#T39" target="_self">Th39</a></i>;<br/><a NAME="E4:67_2"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="vectsp_1.html#K4" target="_self">"</a> </span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></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">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="vectsp_1.html#D19" target="_self">Def19</a></i>;<br/><a NAME="E5:67_2"/><b>then </b>
 <a href="group_1.html#K2">1.</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></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">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="vectsp_1.html#E1:67"><i><font color="Green">E28</font></i></a>, <a class="ref" href="vectsp_1.html#D22" target="_self">Def22</a></i>;<br/><a NAME="E6:67_2"/><b>then </b>
 <a href="group_1.html#K2">1.</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="vectsp_1.html#T39" target="_self">Th39</a></i>;<br/><b>hence </b><a NAME="E7:67_2"/>
contradiction
 <b>by </b><i><a class="ref" href="vectsp_1.html#D21" target="_self">Def21</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:67"/>
contradiction
 <b>by </b><i><a class="txt" href="vectsp_1.html#E2:67"><i><font color="Green">E29</font></i></a>, <a class="txt" href="vectsp_1.html#E3:67"><i><font color="Green">E30</font></i></a></i>;<br/>


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