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

theorem
  i <= j & k <= j & i = j -' k + l implies k = j -' i + l
proof
  assume that
A1: i <= j and
A2: k <= j & i = j -' k + l;
  i - l = j - k by A2,XREAL_1:233;
  hence k = j - i + l .= j -' i + l by A1,XREAL_1:233;
end;
