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

theorem Th47:
  Fib (k) = 1 iff k = 1 or k = 2
proof
  Fib (k) = 1 implies k = 1 or k = 2
  proof
    assume
A1: Fib (k) = 1;
    assume that
A2: not k = 1 and
A3: not k = 2;
A4: k < 2 or k > 2 by A3,XXREAL_0:1;
    k = 0 or k > 1 by A2,NAT_2:19;
    hence contradiction by A1,A4,Th21,Th46,PRE_FF:1;
  end;
  hence thesis by Th21,PRE_FF:1;
end;
