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<div class="add">

<a NAME="E1:68"/>
<span class="p1">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="vectsp_1.html#K3" target="_self">F_Real</a> </span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="vectsp_1.html#K3" target="_self">F_Real</a> </span>)</span> <a href="hidden.html#R1">=</a> 1 <a href="binop_2.html#K23">+</a> 1
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="68_1"><b>proof </b></a><div class="add">

<b>reconsider </b><font color="Maroon">c<sub>2</sub></font> = 1 as    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K1">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="struct_0.html#NM1">Element</a> of <a href="vectsp_1.html#K3" target="_self">F_Real</a>  ;<br/>
<a NAME="E3:68_1"/>
<span class="p1">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="vectsp_1.html#K3" target="_self">F_Real</a> </span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="vectsp_1.html#K3" target="_self">F_Real</a> </span>)</span> <a href="hidden.html#R1">=</a> the <a href="rlvect_1.html#U1">add</a> of <a href="vectsp_1.html#K3" target="_self">F_Real</a>  <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="vectsp_1.html#E30"><i><font color="Green">Lemma9</font></i></a>, <a class="ref" href="rlvect_1.html#T5">RLVECT_1:5</a></i>;<br/>
<b>hence </b><a NAME="E4:68_1"/>
<span class="p1">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="vectsp_1.html#K3" target="_self">F_Real</a> </span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="vectsp_1.html#K3" target="_self">F_Real</a> </span>)</span> <a href="hidden.html#R1">=</a> 1 <a href="binop_2.html#K23">+</a> 1
 <b>by </b><i><a class="ref" href="binop_2.html#D9">BINOP_2:def 9</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:68"/>
<span class="p1">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="vectsp_1.html#K3" target="_self">F_Real</a> </span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="vectsp_1.html#K3" target="_self">F_Real</a> </span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <a href="vectsp_1.html#K3" target="_self">F_Real</a> 
 ;<br/>


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