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

<b>let </b><font color="Maroon">IT</font> be   <a href="binop_1.html#NM2">BinOp</a> of <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="finsub_1.html#K5">Fin</a> <font color="Maroon">A</font></span>)</span>,<span class="p2">(<span class="default"><a href="finsub_1.html#K5">Fin</a> <font color="Maroon">A</font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>, <font color="Maroon">IT'</font> be   <a href="binop_1.html#NM2">BinOp</a> of <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="finsub_1.html#K5">Fin</a> <font color="Maroon">A</font></span>)</span>,<span class="p2">(<span class="default"><a href="finsub_1.html#K5">Fin</a> <font color="Maroon">A</font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>;<br/>

<b>assume </b><a NAME="E1:20_1_2"/><i><font color="Green">E21</font></i>: 
( ( for <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="subset_1.html#M1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="finsub_1.html#K5">Fin</a> <font color="Maroon">A</font></span>)</span>,<span class="p2">(<span class="default"><a href="finsub_1.html#K5">Fin</a> <font color="Maroon">A</font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span> holds  <font color="Maroon">IT</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="normform.html#K3">\</a> <font color="Olive">b</font> ) &amp; ( for <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="subset_1.html#M1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="finsub_1.html#K5">Fin</a> <font color="Maroon">A</font></span>)</span>,<span class="p2">(<span class="default"><a href="finsub_1.html#K5">Fin</a> <font color="Maroon">A</font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span> holds  <font color="Maroon">IT'</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="normform.html#K3">\</a> <font color="Olive">b</font> ) )
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">a</font> be    <a href="subset_1.html#M1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="finsub_1.html#K5">Fin</a> <font color="Maroon">A</font></span>)</span>,<span class="p2">(<span class="default"><a href="finsub_1.html#K5">Fin</a> <font color="Maroon">A</font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>, <font color="Maroon">b</font> be    <a href="subset_1.html#M1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="finsub_1.html#K5">Fin</a> <font color="Maroon">A</font></span>)</span>,<span class="p2">(<span class="default"><a href="finsub_1.html#K5">Fin</a> <font color="Maroon">A</font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>;<br/><a NAME="E1:20_1_2_1"/>
( <font color="Maroon">IT</font> <a href="binop_1.html#K2">.</a> <font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="normform.html#K3">\</a> <font color="Maroon">b</font> &amp; <font color="Maroon">IT'</font> <a href="binop_1.html#K2">.</a> <font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="normform.html#K3">\</a> <font color="Maroon">b</font> )
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E2:20_1_2_1"/>
<font color="Maroon">IT</font> <a href="binop_1.html#K2">.</a> <font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">IT'</font> <a href="binop_1.html#K2">.</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:20_1_2"/>
<font color="Maroon">IT</font> <a href="hidden.html#R1">=</a> <font color="Maroon">IT'</font>
 <b>by </b><i><a class="ref" href="binop_1.html#T2">BINOP_1:2</a></i>;<br/>


</div>
