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<b>let </b><font color="Maroon">f1</font> be   <a href="binop_1.html#NM2">BinOp</a> of  <a href="numbers.html#K5">NAT</a> , <font color="Maroon">f2</font> be   <a href="binop_1.html#NM2">BinOp</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:1_1_2"/><i><font color="Green">E30</font></i>: 
for <font color="Olive">m</font>, <font color="Olive">n</font> being  <a href="nat_1.html#NM1">Nat</a> holds  <font color="Maroon">f1</font> <a href="binop_1.html#K1">.</a> <font color="Olive">m</font>,<font color="Olive">n</font> <a href="hidden.html#R1">=</a> <font color="Olive">m</font> <a href="nat_1.html#K10">hcf</a> <font color="Olive">n</font>
 <b>and </b><br/><a NAME="E2:1_1_2"/><i><font color="Green">E31</font></i>: 
for <font color="Olive">m</font>, <font color="Olive">n</font> being  <a href="nat_1.html#NM1">Nat</a> holds  <font color="Maroon">f2</font> <a href="binop_1.html#K1">.</a> <font color="Olive">m</font>,<font color="Olive">n</font> <a href="hidden.html#R1">=</a> <font color="Olive">m</font> <a href="nat_1.html#K10">hcf</a> <font color="Olive">n</font>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="1_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">m</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> , <font color="Maroon">n</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>thus </b><font color="Maroon">f1</font> <a href="binop_1.html#K2">.</a> <font color="Maroon">m</font>,<font color="Maroon">n</font> = 
<font color="Maroon">m</font> <a href="nat_1.html#K10">hcf</a> <font color="Maroon">n</font>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">f2</font> <a href="binop_1.html#K2">.</a> <font color="Maroon">m</font>,<font color="Maroon">n</font>
<b>by </b><i/>
;<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/>


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