Page 1,2: Running example in the Introduction: The invariant is (pc = inc => x = 0) AND (pc = dec => (x = 0 OR x = 2)) and not (pc = inc => x = 0) AND (pc = dec => x = 2). Page 8: Lemma 4 and subsequent remarks: Lemma 4 assumes that the $R$-Simplify function is equiv- alence preserving. Later, in Section 4.3, we say that R-Simplify can weaken a formula. The correctness with the weakening is outlined later. However, Lemma 5, Lemma 6 and Theorem 2 hold true in the case when R-Simplify weakens a formula. Page 9: Lemma 6: $\psi$ is not contained in Reach, but only has a nonempty intersection with $Reach$. Page 9: Just before description of the InvGen procedure: It says that $\psi$ is an under-approximation and $phi$ an over-approximation of the reachable state set. If we use R-Simplify in propagation, as described in the paper and assume it is not equivalence preserving, then this is no longer true. But, this doesnot effect the correctness (Theorem 2) of the procedure. Theorem 3, Page 11: In a downward iteration sequence with narrowing, we can apply simplification rule (i.e. R-Simplify) only after a propagation step and not after a narrowing step. (The statement of Theorem 3 is more general and suggests that we can R-Simplify any formula in a downward iteration sequence, which is not true.)