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

<b>consider </b><font color="Maroon">ADD</font> being   <a href="binop_1.html#NM2">BinOp</a> of  <a href="euclid.html#K1">REAL</a> <font color="Maroon">n</font><b> such that </b><br/><a NAME="E2:3_1_1"/><i><font color="Green">E33</font></i>: 
( ( for <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="finseq_2.html#M2">Element</a> of  <a href="euclid.html#K1">REAL</a> <font color="Maroon">n</font> holds  <font color="Maroon">ADD</font> <a href="binop_1.html#K2">.</a> <font color="Olive">a</font>,<font color="Olive">b</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="euclid.html#K7">+</a> <font color="Olive">b</font> ) &amp; <font color="Maroon">ADD</font> is <a href="binop_1.html#V1">commutative</a> &amp; <font color="Maroon">ADD</font> is <a href="binop_1.html#V2">associative</a> )
 <b>by </b><i/>;<br/>
<b>take </b>
<font color="Maroon">ADD</font>
;<br/>

<b>thus </b><a NAME="E3:3_1_1"/>
for <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="finseq_2.html#M2">Element</a> of  <a href="euclid.html#K1">REAL</a> <font color="Maroon">n</font> holds  <font color="Maroon">ADD</font> <a href="binop_1.html#K2">.</a> <font color="Olive">a</font>,<font color="Olive">b</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="euclid.html#K7">+</a> <font color="Olive">b</font>
 <b>by </b><i/>;<br/>


</div>
