reserve n, k, r, m, i, j for Nat;

theorem Th67:
  for n being Element of NAT holds Fib (n), Fib (n+1) are_coprime
proof
  let n be Element of NAT;
A1: n,n + 1 are_coprime by PEPIN:1;
  Fib (n) gcd Fib (n + 1) = Fib (n gcd (n + 1)) by FIB_NUM:5
    .= 1 by A1,INT_2:def 3,PRE_FF:1;
  hence thesis by INT_2:def 3;
end;
