let f1, f2 be BinOp of NAT ; :: thesis: ( ( for m, n being Nat holds f1 . m,n = m lcm n ) & ( for m, n being Nat holds f2 . m,n = m lcm n ) implies f1 = f2 )
assume that
A5: for m, n being Nat holds f1 . m,n = m lcm n and
A6: for m, n being Nat holds f2 . m,n = m lcm n ; :: thesis: f1 = f2

now

let m, n be Element of NAT ; :: thesis: f1 . m,n = f2 . m,n
thus f1 . m,n = m lcm n by A5
.= f2 . m,n by A6 ; :: thesis: verum

end;

hence f1 = f2 by BINOP_1:2; :: thesis: verum