
theorem LmA:
  for n,k be Nat st k in Segm (n+1) holds n - k is Nat
  proof
    let n,k be Nat such that
    A1: k in Segm (n+1);
    (n+1) > k by A1,NAT_1:44; then
    n >= k by NAT_1:13; then
    n - k >= k - k by XREAL_1:9;
    hence thesis by INT_1:3;
  end;
