A note on Darwiche and Pearl

It is shown that Darwiche and Pearl's postulates imply an interesting property, not noticed by the authors. In [?], Darwiche and Pearl propose postulates for iterated revisions, noted (R*1) to (R*6) and (C1) to (C4). In particular, the postulate (C3) reads: (C3) If Ψ • α |= µ, then (Ψ • µ) • α |= µ. It will be shown that, in the presence (R*1) to (R*6), (C1) and (C3) imply: (* *) If Ψ • α |= µ, then (Ψ • µ) • α ≡ Ψ • α.