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

theorem
  for n being non zero Element of NAT holds n -' 1 + 2 = n + 1
proof
  let n be non zero Element of NAT;
  n >= 1 by NAT_2:19;
  then n -' 1 + 2 = n + 2 -' 1 by NAT_D:38
    .= n + 2 - 1 by NAT_D:37;
  hence thesis;
end;
