Hint Rewrite @lift0_exp : norm2.
Hint Rewrite @lift0C_exp : norm2.

(* Specifications: *)
Lemma lift0_andp {A}{NA: NatDed A}:
forall P Q,
lift0 (@andp A NA P Q) = andp (lift0 P) (lift0 Q).
Lemma lift0C_andp {A}{NA: NatDed A}:
forall P Q: A,
`(@andp A NA P Q) =
andp (`P) (`Q).
Lemma lift0_prop {A}{NA: NatDed A}:
forall P, lift0 (!! P) = !!P.
Lemma lift0C_sepcon {A}{NA: NatDed A}{SA: SepLog A}:
forall P Q N2 S2,
(@liftx (LiftEnviron A) (@sepcon A N2 S2 P Q)) =
(@sepcon (environ->A) _ _
(@liftx (LiftEnviron A) P)
(@liftx (LiftEnviron A) Q)).
Lemma derives_extract_PROP :
forall (P1: Prop) A P QR S,
(P1 -> A && PROPx P QR |-- S) ->
A && PROPx (P1::P) QR |-- S.