
theorem Th2:
  for n being Nat st n >= 1 holds n -' 1 <= 2 * n -' 2
proof
  let n be Nat;
  assume
A1: n >= 1;
  then 2 * 1 <= 2 * n by XREAL_1:64;
  then
A2: 1 * (n -' 1) <= 2 * (n -' 1) & 2 * n -' 2 = 2 * n - 2 by XREAL_1:64,233;
  n -' 1 = n - 1 by A1,XREAL_1:233;
  hence thesis by A2;
end;
