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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="vectsp_1.html#NM2">Field</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="vectsp_1.html#NM6">VectSp</a> of <font color="Maroon">c<sub>1</sub></font>;<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>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>2</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>5</sub></font> be    <a href="vectsp_4.html#M1" target="_self">Subspace</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>









<b>assume </b><b>that </b><br/><a NAME="E1:56"/><i><font color="Green">E41</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>1</sub></font>
 <b>and </b><br/><a NAME="E2:56"/><i><font color="Green">E42</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="vectsp_1.html#K6">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="vectsp_4.html#K3" target="_self">+</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>5</sub></font>
 ;<br/>

<b>assume </b><a NAME="E3:56"/>
not <font color="Maroon">c<sub>4</sub></font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">c<sub>5</sub></font>
 ;<br/>

<a NAME="E4:56"/><b>then </b>
not <span class="p1">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="vectsp_1.html#K6">*</a> <font color="Maroon">c<sub>4</sub></font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="ref" href="vectsp_1.html#D26">VECTSP_1:def 26</a></i>;<br/>
<a NAME="E5:56"/><b>then </b>
not <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="vectsp_1.html#K4">"</a> </span>)</span> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="vectsp_1.html#K6">*</a> <font color="Maroon">c<sub>4</sub></font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="vectsp_4.html#E1:56"><i><font color="Green">E41</font></i></a>, <a class="ref" href="vectsp_1.html#D22">VECTSP_1:def 22</a></i>;<br/>
<a NAME="E6:56"/><b>then </b>
not <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="vectsp_1.html#K4">"</a> </span>)</span> <a href="vectsp_1.html#K6">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="vectsp_1.html#K6">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="ref" href="vectsp_1.html#D26">VECTSP_1:def 26</a></i>;<br/>
<a NAME="E7:56"/><b>then </b><i><font color="Green">E43</font></i>: 
not <font color="Maroon">c<sub>3</sub></font> <a href="vectsp_1.html#K6">*</a> <font color="Maroon">c<sub>4</sub></font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="ref" href="vectsp_4.html#T29" target="_self">Th29</a></i>;<br/>
<a NAME="E8:56"/>
(  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>2</sub></font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">c<sub>5</sub></font> &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="vectsp_1.html#K6">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <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>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="vectsp_1.html#K6">*</a> <font color="Maroon">c<sub>4</sub></font> )
 
<b>by </b><i><a class="ref" href="vectsp_4.html#T25" target="_self">Th25</a>, <a class="ref" href="rlvect_1.html#T10">RLVECT_1:10</a></i>;<br/>
<a NAME="E9:56"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="vectsp_1.html#K6">*</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="vectsp_1.html#K6">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <font color="Olive">b<sub>1</sub></font></span>)</span> where B is   <a href="vectsp_1.html#NM5">Vector</a> of <font color="Maroon">c<sub>2</sub></font> : <font color="Olive">b<sub>1</sub></font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">c<sub>5</sub></font> </span>}</span> 
 
;<br/>
<a NAME="E10:56"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="vectsp_1.html#K6">*</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="vectsp_4.html#E2:56"><i><font color="Green">E42</font></i></a></i>;<br/>
<b>hence </b><a NAME="E11:56"/>
contradiction
 <b>by </b><i><a class="txt" href="vectsp_4.html#E7:56"><i><font color="Green">E43</font></i></a>, <a class="ref" href="rlvect_1.html#D1">RLVECT_1:def 1</a></i>;<br/>


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