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

theorem Th29:
  for n being Nat holds Fib (n + 1) = Fib (n + 2) - Fib (n)
proof
  let n be Nat;
  Fib (n+2) - Fib (n) = Fib (n+1+1) - Fib (n)
    .= Fib (n) + Fib (n+1) - Fib (n) by PRE_FF:1
    .= Fib (n+1);
  hence thesis;
end;
