reserve i, j, k, l, m, n, t for Nat;

theorem
  j < i implies i -' (j + 1) + 1 = i -' j
proof
  assume
A1: j < i;
  then j + 1 <= i by NAT_1:13;
  hence i -' (j + 1) + 1 = i - (j + 1) + 1 by XREAL_1:233
    .= i - j
    .= i -' j by A1,XREAL_1:233;
end;
