<?xml version="1.0"?>
<div class="add">

<b>thus </b><a NAME="E1:16"/>
for <font color="Olive">r</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K1">REAL</a>  holds  <a href="binop_2.html#K33" target="_self">addreal</a>  <a href="binop_1.html#K2">.</a> 0,<font color="Olive">r</font> <a href="hidden.html#R1">=</a> <font color="Olive">r</font>
  <i><font color="Red">:: according to </font></i><a class="ref" href="binop_1.html#D7">BINOP_1:def 7</a>,<a class="ref" href="binop_1.html#D16">BINOP_1:def 16</a><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">r</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K1">REAL</a> ;<br/>

<b>thus </b><a href="binop_2.html#K33" target="_self">addreal</a>  <a href="binop_1.html#K2">.</a> 0,<font color="Maroon">r</font> = 
0 <a href="binop_2.html#K9" target="_self">+</a> <font color="Maroon">r</font>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">r</font>

;<br/>


</div><b>end;</b></div>

<b>let </b><font color="Maroon">r</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K1">REAL</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="binop_1.html#D17">BINOP_1:def 17</a><br/>

<b>thus </b><a href="binop_2.html#K33" target="_self">addreal</a>  <a href="binop_1.html#K2">.</a> <font color="Maroon">r</font>,0 = 
<font color="Maroon">r</font> <a href="binop_2.html#K9" target="_self">+</a> 0
<b>by </b><i/>
<br/>.= 
<font color="Maroon">r</font>

;<br/>


</div>
