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<b>let </b><font color="Maroon">F</font> be   <a href="vectsp_1.html#NM2">Field</a>;<br/><b>let </b><font color="Maroon">S</font> be   <a href="symsp_1.html#NM1">SymSp</a> of <font color="Maroon">F</font>;<br/><b>let </b><font color="Maroon">b</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">S</font>;<br/><b>let </b><font color="Maroon">a</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">S</font>;<br/><b>let </b><font color="Maroon">l</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">F</font>;<br/>









<b>set </b><font color="Maroon">1F</font> =  <a href="group_1.html#K2">1.</a> <font color="Maroon">F</font>;<br/>
<b>assume </b><a NAME="E1:17"/><i><font color="Green">E27</font></i>: 
( not <font color="Maroon">b</font> <a href="symsp_1.html#R1" target="_self">_|_</a> <font color="Maroon">a</font> &amp; not <font color="Maroon">l</font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">F</font> )
 ;<br/>

<div><i><font color="Green">E31</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">E32</font></i>: 
<font color="Maroon">l</font> <a href="vectsp_1.html#K6">*</a> <font color="Maroon">b</font> <a href="symsp_1.html#R1" target="_self">_|_</a> <font color="Maroon">a</font>
 ;<br/><b>consider </b><font color="Maroon">k</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">F</font><b> such that </b><br/><a NAME="E3:17_1"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">l</font> <a href="group_1.html#K10">*</a> <font color="Maroon">k</font> <a href="hidden.html#R1">=</a>  <a href="group_1.html#K2">1.</a> <font color="Maroon">F</font>
 <b>by </b><i>, <a class="ref" href="vectsp_1.html#D20">VECTSP_1:def 20</a></i>;<br/><a NAME="E4:17_1"/>
<font color="Maroon">k</font> <a href="vectsp_1.html#K6">*</a> <span class="p1">(<span class="default"><font color="Maroon">l</font> <a href="vectsp_1.html#K6">*</a> <font color="Maroon">b</font></span>)</span> <a href="symsp_1.html#R1" target="_self">_|_</a> <font color="Maroon">a</font>
 <b>by </b><i>, </i>;<br/><a NAME="E5:17_1"/><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="vectsp_1.html#K6">*</a> <font color="Maroon">b</font> <a href="symsp_1.html#R1" target="_self">_|_</a> <font color="Maroon">a</font>
 <b>by </b><i>, <a class="ref" href="vectsp_1.html#D26">VECTSP_1:def 26</a></i>;<br/><b>hence </b><a NAME="E6:17_1"/>
contradiction
 <b>by </b><i>, <a class="ref" href="vectsp_1.html#D26">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">b</font> <a href="symsp_1.html#R1" target="_self">_|_</a> <font color="Maroon">l</font> <a href="vectsp_1.html#K6">*</a> <font color="Maroon">a</font>
 ;<br/><a NAME="E2:17_2"/><b>then </b><i><font color="Green">E35</font></i>: 
<font color="Maroon">l</font> <a href="vectsp_1.html#K6">*</a> <font color="Maroon">a</font> <a href="symsp_1.html#R1" target="_self">_|_</a> <font color="Maroon">b</font>
 <b>by </b><i/>;<br/><b>consider </b><font color="Maroon">k</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">F</font><b> such that </b><br/><a NAME="E4:17_2"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">l</font> <a href="group_1.html#K10">*</a> <font color="Maroon">k</font> <a href="hidden.html#R1">=</a>  <a href="group_1.html#K2">1.</a> <font color="Maroon">F</font>
 <b>by </b><i>, <a class="ref" href="vectsp_1.html#D20">VECTSP_1:def 20</a></i>;<br/><a NAME="E5:17_2"/>
<font color="Maroon">k</font> <a href="vectsp_1.html#K6">*</a> <span class="p1">(<span class="default"><font color="Maroon">l</font> <a href="vectsp_1.html#K6">*</a> <font color="Maroon">a</font></span>)</span> <a href="symsp_1.html#R1" target="_self">_|_</a> <font color="Maroon">b</font>
 <b>by </b><i>, </i>;<br/><a NAME="E6:17_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="vectsp_1.html#K6">*</a> <font color="Maroon">a</font> <a href="symsp_1.html#R1" target="_self">_|_</a> <font color="Maroon">b</font>
 <b>by </b><i>, <a class="ref" href="vectsp_1.html#D26">VECTSP_1:def 26</a></i>;<br/><a NAME="E7:17_2"/><b>then </b>
<font color="Maroon">a</font> <a href="symsp_1.html#R1" target="_self">_|_</a> <font color="Maroon">b</font>
 <b>by </b><i><a class="ref" href="vectsp_1.html#D26">VECTSP_1:def 26</a></i>;<br/><b>hence </b><a NAME="E8:17_2"/>
contradiction
 <b>by </b><i>, </i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:17"/>
( not <font color="Maroon">l</font> <a href="vectsp_1.html#K6">*</a> <font color="Maroon">b</font> <a href="symsp_1.html#R1" target="_self">_|_</a> <font color="Maroon">a</font> &amp; not <font color="Maroon">b</font> <a href="symsp_1.html#R1" target="_self">_|_</a> <font color="Maroon">l</font> <a href="vectsp_1.html#K6">*</a> <font color="Maroon">a</font> )
 <b>by </b><i/>;<br/>


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