## 1 A short remark

In [DarwPearl:AIJ], Darwiche and Pearl propose postulates for iterated revisions, noted (R*1) to (R*6) and (C1) to (C4). In particular, the postulate (C3) reads:

It will be shown that, in the presence (R*1) to (R*6), (C1) and (C3) imply:

First, a lemma.

###### Lemma 1

Assuming (R*1) to (R*6), if , then .

Proof: Since , . By (R*4), . Therefore .

If is satisfiable, then, since , is satisfiable and, by (R*5), and therefore .

If is not satisfiable, then, by (R*3), is not satisfiable, and is not satisfiable. By (R*1), then, .

###### Lemma 2

Assuming (R*1) to (R*6), (C1) and (C3), if , then .

We conclude that .