
theorem Th3:
  for n being Nat st n > 1 holds n < 2 * n -' 1
proof
  let n be Nat;
  assume
A1: n > 1;
  then n + n > n + 1 by XREAL_1:6;
  then
A2: n + n - 1 > n + 1 - 1 by XREAL_1:9;
  1 * 2 < 2 * n by A1,XREAL_1:68;
  hence thesis by A2,XREAL_1:233,XXREAL_0:2;
end;
