Section sec_map_modalop.
Variable A B: Type.
Proof using.
unfold and_tl; intuition.
Qed.
Proof using.
unfold and_tl; intuition.
Qed.
Proof using.
unfold or_tl; intuition.
Qed.
Proof using.
unfold or_tl; intuition.
Qed.
Proof using.
unfold impl_tl; intuition.
Qed.
Proof using.
unfold impl_tl; intuition.
Qed.
Proof using.
unfold not_tl; intuition.
Qed.
Proof using.
unfold not_tl; intuition.
Qed.
Proof using.
intros f P (x, s) nP; assumption.
Qed.
Proof using.
intros f P (x, s) nP; assumption.
Qed.
Proof using.
intros f P Q PQ [x s]; apply PQ.
Qed.

Lemma next_map_conv :
forall (f: A->B) (P: infseq A->Prop) (Q: infseq B->Prop),
(forall s, Q (map f s) -> P s) ->
forall (s: infseq A), next Q (map f s) -> next P s.