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