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

<b>let </b><font color="Maroon">f1</font> be   <a href="binop_1.html#NM2">BinOp</a> of  <a href="numbers.html#K1">REAL</a> , <font color="Maroon">f2</font> be   <a href="binop_1.html#NM2">BinOp</a> of  <a href="numbers.html#K1">REAL</a> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:1_1_2"/><i><font color="Green">E25</font></i>: 
for <font color="Olive">x</font>, <font color="Olive">y</font> being  <a href="real_1.html#NM1">Real</a> holds  <font color="Maroon">f1</font> <a href="binop_1.html#K2">.</a> <font color="Olive">x</font>,<font color="Olive">y</font> <a href="hidden.html#R1">=</a>  <a href="square_1.html#K1">min</a> <font color="Olive">x</font>,<font color="Olive">y</font>
 <b>and </b><br/><a NAME="E2:1_1_2"/><i><font color="Green">E26</font></i>: 
for <font color="Olive">x</font>, <font color="Olive">y</font> being  <a href="real_1.html#NM1">Real</a> holds  <font color="Maroon">f2</font> <a href="binop_1.html#K2">.</a> <font color="Olive">x</font>,<font color="Olive">y</font> <a href="hidden.html#R1">=</a>  <a href="square_1.html#K1">min</a> <font color="Olive">x</font>,<font color="Olive">y</font>
 ;<br/>

<a NAME="E3:1_1_2"/>
for <font color="Olive">x</font>, <font color="Olive">y</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K1">REAL</a>  holds  <font color="Maroon">f1</font> <a href="binop_1.html#K2">.</a> <font color="Olive">x</font>,<font color="Olive">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f2</font> <a href="binop_1.html#K2">.</a> <font color="Olive">x</font>,<font color="Olive">y</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="1_1_2_1"><b>proof </b></a><div class="add">

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

<a NAME="E1:1_1_2_1"/>
( <font color="Maroon">f1</font> <a href="binop_1.html#K2">.</a> <font color="Maroon">x</font>,<font color="Maroon">y</font> <a href="hidden.html#R1">=</a>  <a href="square_1.html#K1">min</a> <font color="Maroon">x</font>,<font color="Maroon">y</font> &amp; <font color="Maroon">f2</font> <a href="binop_1.html#K2">.</a> <font color="Maroon">x</font>,<font color="Maroon">y</font> <a href="hidden.html#R1">=</a>  <a href="square_1.html#K1">min</a> <font color="Maroon">x</font>,<font color="Maroon">y</font> )
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E2:1_1_2_1"/>
<font color="Maroon">f1</font> <a href="binop_1.html#K2">.</a> <font color="Maroon">x</font>,<font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f2</font> <a href="binop_1.html#K2">.</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>
 ;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:1_1_2"/>
<font color="Maroon">f1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f2</font>
 <b>by </b><i><a class="ref" href="binop_1.html#T2">BINOP_1:2</a></i>;<br/>


</div>
