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<b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="vectsp_1.html#NM2">Field</a>;<br/><b>let </b><font color="Maroon">c<sub>5</sub></font> be   <a href="symsp_1.html#NM1">SymSp</a> of <font color="Maroon">c<sub>4</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>6</sub></font>, <font color="Maroon">c<sub>7</sub></font>, <font color="Maroon">c<sub>8</sub></font>, <font color="Maroon">c<sub>9</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>5</sub></font>;<br/>











<b>set </b><font color="Maroon">c<sub>10</sub></font> =  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>5</sub></font>;<br/>
<b>assume </b><a NAME="E1:20"/><i><font color="Green">E16</font></i>: 
( not <font color="Maroon">c<sub>6</sub></font> <a href="symsp_1.html#R1" target="_self">_|_</a> <font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="symsp_1.html#R1" target="_self">_|_</a> <font color="Maroon">c<sub>8</sub></font> &amp; not <font color="Maroon">c<sub>9</sub></font> <a href="symsp_1.html#R1" target="_self">_|_</a> <font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>9</sub></font> <a href="symsp_1.html#R1" target="_self">_|_</a> <font color="Maroon">c<sub>7</sub></font> )
 ;<br/>

<b>assume </b><a NAME="E2:20"/>
( <font color="Maroon">c<sub>6</sub></font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>9</sub></font> <a href="symsp_1.html#R1" target="_self">_|_</a> <font color="Maroon">c<sub>7</sub></font> or <font color="Maroon">c<sub>6</sub></font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>9</sub></font> <a href="symsp_1.html#R1" target="_self">_|_</a> <font color="Maroon">c<sub>8</sub></font> )
 ;<br/>

<a NAME="E3:20"/><b>then </b>
( ( <font color="Maroon">c<sub>6</sub></font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>9</sub></font> <a href="symsp_1.html#R1" target="_self">_|_</a> <font color="Maroon">c<sub>7</sub></font> &amp; <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>4</sub></font></span>)</span></span>)</span> <a href="vectsp_1.html#K6">*</a> <font color="Maroon">c<sub>9</sub></font> <a href="symsp_1.html#R1" target="_self">_|_</a> <font color="Maroon">c<sub>7</sub></font> ) or ( <font color="Maroon">c<sub>6</sub></font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>9</sub></font> <a href="symsp_1.html#R1" target="_self">_|_</a> <font color="Maroon">c<sub>8</sub></font> &amp; <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>4</sub></font></span>)</span></span>)</span> <a href="vectsp_1.html#K6">*</a> <font color="Maroon">c<sub>6</sub></font> <a href="symsp_1.html#R1" target="_self">_|_</a> <font color="Maroon">c<sub>8</sub></font> ) )
 
<b>by </b><i><a class="txt" href="symsp_1.html#E1:20"><i><font color="Green">E16</font></i></a>, <a class="ref" href="symsp_1.html#D2" target="_self">Def2</a></i>;<br/>
<a NAME="E4:20"/><b>then </b>
( ( <font color="Maroon">c<sub>6</sub></font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>9</sub></font> <a href="symsp_1.html#R1" target="_self">_|_</a> <font color="Maroon">c<sub>7</sub></font> &amp;  <a href="rlvect_1.html#K5">-</a> <font color="Maroon">c<sub>9</sub></font> <a href="symsp_1.html#R1" target="_self">_|_</a> <font color="Maroon">c<sub>7</sub></font> ) or ( <font color="Maroon">c<sub>6</sub></font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>9</sub></font> <a href="symsp_1.html#R1" target="_self">_|_</a> <font color="Maroon">c<sub>8</sub></font> &amp;  <a href="rlvect_1.html#K5">-</a> <font color="Maroon">c<sub>6</sub></font> <a href="symsp_1.html#R1" target="_self">_|_</a> <font color="Maroon">c<sub>8</sub></font> ) )
 
<b>by </b><i><a class="ref" href="vectsp_1.html#T59">VECTSP_1:59</a></i>;<br/>
<a NAME="E5:20"/><b>then </b>
( <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K5">-</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="symsp_1.html#R1" target="_self">_|_</a> <font color="Maroon">c<sub>7</sub></font> or <span class="p1">(<span class="default"><a href="rlvect_1.html#K5">-</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="symsp_1.html#R1" target="_self">_|_</a> <font color="Maroon">c<sub>8</sub></font> )
 
<b>by </b><i><a class="ref" href="symsp_1.html#D2" target="_self">Def2</a></i>;<br/>
<a NAME="E6:20"/><b>then </b>
( <font color="Maroon">c<sub>6</sub></font> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></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<sub>9</sub></font></span>)</span></span>)</span> <a href="symsp_1.html#R1" target="_self">_|_</a> <font color="Maroon">c<sub>7</sub></font> or <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rlvect_1.html#K5">-</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>9</sub></font> <a href="symsp_1.html#R1" target="_self">_|_</a> <font color="Maroon">c<sub>8</sub></font> )
 
<b>by </b><i><a class="ref" href="rlvect_1.html#D6">RLVECT_1:def 6</a></i>;<br/>
<a NAME="E7:20"/><b>then </b>
( <font color="Maroon">c<sub>6</sub></font> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="symsp_1.html#R1" target="_self">_|_</a> <font color="Maroon">c<sub>7</sub></font> or <span class="p1">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>9</sub></font> <a href="symsp_1.html#R1" target="_self">_|_</a> <font color="Maroon">c<sub>8</sub></font> )
 
<b>by </b><i><a class="ref" href="rlvect_1.html#T16">RLVECT_1:16</a></i>;<br/>
<b>hence </b><a NAME="E8:20"/>
contradiction
 <b>by </b><i><a class="txt" href="symsp_1.html#E1:20"><i><font color="Green">E16</font></i></a>, <a class="ref" href="rlvect_1.html#T10">RLVECT_1:10</a></i>;<br/>


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