
theorem Th1:
  for k,n being Nat st k < n & 3 <= n holds k+1 < n or 2 <= k
proof
  let k,n be Nat such that
A1: k < n and
A2: 3 <= n;
  assume
A3: k+1 >= n;
  k+1 <= n by A1,NAT_1:13;
  then 3 <= k+1 by A2,A3,XXREAL_0:1;
  then 3-1 <= k+1-1 by XREAL_1:9;
  hence thesis;
end;
