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<b>let </b><font color="Maroon" title="c1">f1</font>, <font color="Maroon" title="c2">f2</font> be   <a href="binop_1.html#NM2" title="BINOP_1:NM.2">BinOp</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:1_2_2"/><i><font color="Green" title="E1">A5</font></i>: 
for <font color="Olive" title="b1">m</font>, <font color="Olive" title="b2">n</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> holds  <font color="Maroon" title="c1">f1</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Olive" title="b1">m</font>,<font color="Olive" title="b2">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">m</font> <a href="nat_d.html#K6" title="NAT_D:func.6">lcm</a> <font color="Olive" title="b2">n</font>
 <b>and </b><br/><a NAME="E2:1_2_2"/><i><font color="Green" title="E2">A6</font></i>: 
for <font color="Olive" title="b1">m</font>, <font color="Olive" title="b2">n</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> holds  <font color="Maroon" title="c2">f2</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Olive" title="b1">m</font>,<font color="Olive" title="b2">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">m</font> <a href="nat_d.html#K6" title="NAT_D:func.6">lcm</a> <font color="Olive" title="b2">n</font>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="1_2_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c3">m</font>, <font color="Maroon" title="c4">n</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>thus </b><font color="Maroon" title="c1">f1</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c3">m</font>,<font color="Maroon" title="c4">n</font> = 
<font color="Maroon" title="c3">m</font> <a href="nat_d.html#K6" title="NAT_D:func.6">lcm</a> <font color="Maroon" title="c4">n</font>
<b>by </b><i><a class="txt" href="nat_lat.html#E1:1_2_2"><i><font color="Green" title="E1">A5</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c2">f2</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c3">m</font>,<font color="Maroon" title="c4">n</font>
<b>by </b><i><a class="txt" href="nat_lat.html#E2:1_2_2"><i><font color="Green" title="E2">A6</font></i></a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:1_2_2"/>
<font color="Maroon" title="c1">f1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f2</font>
 <b>by </b><i><a class="ref" href="binop_1.html#T2" title="BINOP_1:th.2">BINOP_1:2</a></i>;<br/>


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