
theorem ADDC1:
  for n be Nat holds n <= n!
  proof
    let n be Nat;
    n + 1 <= 3 or 3 <= n by INT_1:7; then
    n + 1 - 1 <= 3 - 1 or 3 <= n by XREAL_1:9; then
CCS:(n = 0 or ... or n = 2) or 3 <= n;
    per cases by CCS;
    suppose n = 0;
      hence thesis;
    end;
    suppose n = 1;
      hence thesis by NEWTON:13;
    end;
    suppose n = 2;
      hence thesis by NEWTON:14;
    end;
    suppose n >= 3;
      hence thesis by ASYMPT_1:59;
    end;
  end;
