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

<b>let </b><font color="Maroon">o1</font> be   <a href="binop_1.html#NM2">BinOp</a> of  <a href="msualg_2.html#K14" target="_self">MSSub</a> <font color="Maroon">U0</font>, <font color="Maroon">o2</font> be   <a href="binop_1.html#NM2">BinOp</a> of  <a href="msualg_2.html#K14" target="_self">MSSub</a> <font color="Maroon">U0</font>;<br/>

<b>assume </b><a NAME="E1:64_1_2"/><i><font color="Green">E22</font></i>: 
( ( for <font color="Olive">x</font>, <font color="Olive">y</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="msualg_2.html#K14" target="_self">MSSub</a> <font color="Maroon">U0</font><br/> for <font color="Olive">U1</font>, <font color="Olive">U2</font> being <a href="msualg_1.html#V4">strict</a>  <a href="msualg_2.html#M1" target="_self">MSSubAlgebra</a> of <font color="Maroon">U0</font>  st <font color="Olive">x</font> <a href="hidden.html#R1">=</a> <font color="Olive">U1</font> &amp; <font color="Olive">y</font> <a href="hidden.html#R1">=</a> <font color="Olive">U2</font> holds <br/><font color="Maroon">o1</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="Olive">U1</font> <a href="msualg_2.html#K11" target="_self">/\</a> <font color="Olive">U2</font> ) &amp; ( for <font color="Olive">x</font>, <font color="Olive">y</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="msualg_2.html#K14" target="_self">MSSub</a> <font color="Maroon">U0</font><br/> for <font color="Olive">U1</font>, <font color="Olive">U2</font> being <a href="msualg_1.html#V4">strict</a>  <a href="msualg_2.html#M1" target="_self">MSSubAlgebra</a> of <font color="Maroon">U0</font>  st <font color="Olive">x</font> <a href="hidden.html#R1">=</a> <font color="Olive">U1</font> &amp; <font color="Olive">y</font> <a href="hidden.html#R1">=</a> <font color="Olive">U2</font> holds <br/><font color="Maroon">o2</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="Olive">U1</font> <a href="msualg_2.html#K11" target="_self">/\</a> <font color="Olive">U2</font> ) )
 ;<br/>

<a NAME="E2:64_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="msualg_2.html#K14" target="_self">MSSub</a> <font color="Maroon">U0</font> holds  <font color="Maroon">o1</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">o2</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="64_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="msualg_2.html#K14" target="_self">MSSub</a> <font color="Maroon">U0</font>, <font color="Maroon">y</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="msualg_2.html#K14" target="_self">MSSub</a> <font color="Maroon">U0</font>;<br/>

<b>reconsider </b><font color="Maroon">U1</font> = <font color="Maroon">x</font>, <font color="Maroon">U2</font> = <font color="Maroon">y</font> as  <a href="msualg_1.html#V4">strict</a>  <a href="msualg_2.html#M1" target="_self">MSSubAlgebra</a> of <font color="Maroon">U0</font> <b>by </b><i><a class="ref" href="msualg_2.html#D3" target="_self">Def3</a></i>;<br/>
<a NAME="E2:64_1_2_1"/>
( <font color="Maroon">o1</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">U1</font> <a href="msualg_2.html#K11" target="_self">/\</a> <font color="Maroon">U2</font> &amp; <font color="Maroon">o2</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">U1</font> <a href="msualg_2.html#K11" target="_self">/\</a> <font color="Maroon">U2</font> )
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E3:64_1_2_1"/>
<font color="Maroon">o1</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">o2</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="E3:64_1_2"/>
<font color="Maroon">o1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">o2</font>
 <b>by </b><i><a class="ref" href="binop_1.html#T2">BINOP_1:2</a></i>;<br/>


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