
theorem Th2:
  for n,m,k being Nat st m <= k & n < m holds k -' m < k -' n
proof
  let n,m,k be Nat such that
A1: m <= k and
A2: n < m;
A3: k - m < k - n by A2,XREAL_1:15;
  k -' n = k - n by A1,A2,XREAL_1:233,XXREAL_0:2;
  hence thesis by A1,A3,XREAL_1:233;
end;
