
theorem
  for i, k being Nat holds 1 <= i & 1 <= k implies (k-'i)+1 <= k
proof
  let i, k be Nat;
  assume that
A1: 1 <= i and
A2: 1 <= k;
  (k-'i) <= k -' 1 by A1,NAT_D:41;
  then (k-'i)+1 <= k -' 1+1 by XREAL_1:6;
  hence thesis by A2,XREAL_1:235;
end;
