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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">a</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">S</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">c</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">S</font>;<br/>









<b>assume </b><a NAME="E1:15"/><i><font color="Green">E27</font></i>: 
( not <font color="Maroon">a</font> <a href="symsp_1.html#R1" target="_self">_|_</a> <font color="Maroon">b</font> &amp; <font color="Maroon">c</font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">a</font> <a href="symsp_1.html#R1" target="_self">_|_</a> <font color="Maroon">b</font> )
 ;<br/>

<b>assume </b><a NAME="E2:15"/>
<font color="Maroon">c</font> <a href="symsp_1.html#R1" target="_self">_|_</a> <font color="Maroon">b</font>
 ;<br/>

<a NAME="E3:15"/><b>then </b>
<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="vectsp_1.html#K6">*</a> <font color="Maroon">c</font> <a href="symsp_1.html#R1" target="_self">_|_</a> <font color="Maroon">b</font>
 
<b>by </b><i/>;<br/>
<a NAME="E4:15"/><b>then </b>
 <a href="rlvect_1.html#K5">-</a> <font color="Maroon">c</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#T59">VECTSP_1:59</a></i>;<br/>
<a NAME="E5:15"/><b>then </b>
<span class="p1">(<span class="default"><a href="rlvect_1.html#K5">-</a> <font color="Maroon">c</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">c</font> <a href="rlvect_1.html#K4">+</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="E6:15"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c</font> <a href="rlvect_1.html#K4">+</a> <span class="p2">(<span class="default"><a href="rlvect_1.html#K5">-</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</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="rlvect_1.html#D6">RLVECT_1:def 6</a></i>;<br/>
<a NAME="E7:15"/><b>then </b>
<span class="p1">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">S</font></span>)</span> <a href="rlvect_1.html#K4">+</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="rlvect_1.html#T16">RLVECT_1:16</a></i>;<br/>
<b>hence </b><a NAME="E8:15"/>
contradiction
 <b>by </b><i>, <a class="ref" href="rlvect_1.html#T10">RLVECT_1:10</a></i>;<br/>


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