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<b>set </b><font color="Maroon">c<sub>1</sub></font> =  <a href="vectsp_1.html#K1">G_Real</a> ;<br/>
<a NAME="E1:2"/><i><font color="Green">E3</font></i>: 
 <a href="rlvect_1.html#K1">0.</a> <a href="vectsp_1.html#K1">G_Real</a>  <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i><a class="ref" href="rlvect_1.html#D2">RLVECT_1:def 2</a></i>;<br/>
<b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <a href="vectsp_1.html#K1">G_Real</a> ;<br/>

<b>assume </b><a NAME="E2:2"/><i><font color="Green">E4</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <a href="vectsp_1.html#K1">G_Real</a> 
 ;<br/>

<b>reconsider </b><font color="Maroon">c<sub>3</sub></font> = <font color="Maroon">c<sub>2</sub></font> as   <a href="real_1.html#NM1">Real</a> ;<br/>
0 = 
the <a href="rlvect_1.html#U1">add</a> of <a href="vectsp_1.html#K1">G_Real</a>  <a href="funct_1.html#K1">.</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K4">]</a></span>
<b>by </b><i><a class="txt" href="tdgroup.html#E1:2"><i><font color="Green">E3</font></i></a>, <a class="txt" href="tdgroup.html#E2:2"><i><font color="Green">E4</font></i></a>, <a class="ref" href="rlvect_1.html#D3">RLVECT_1:def 3</a></i>
<br/>.= 
the <a href="rlvect_1.html#U1">add</a> of <a href="vectsp_1.html#K1">G_Real</a>  <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>3</sub></font>

<br/>.= 
<span class="p1">(<span class="default">1 <a href="binop_2.html#K11">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binop_2.html#K9">+</a> <font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="ref" href="binop_2.html#D9">BINOP_2:def 9</a></i>
<br/>.= 
2 <a href="binop_2.html#K11">*</a> <font color="Maroon">c<sub>3</sub></font>

;<br/>
<b>hence </b><a NAME="E5:2"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <a href="vectsp_1.html#K1">G_Real</a> 
 <b>by </b><i><a class="txt" href="tdgroup.html#E1:2"><i><font color="Green">E3</font></i></a></i>;<br/>


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