Definition hackfun phi0 phi :=
level phi0 = level phi /\ ghost_of phi0 = ghost_of phi /\
forall loc, (identity (phi0 @ loc) <-> identity (phi @ loc)) /\
(~identity (phi0 @ loc) -> (phi0 @ loc = phi @ loc)).

Lemma hackfun_beyond_block:
forall b w w', hackfun w w' -> hackfun (beyond_block b w) (beyond_block b w').