Section sec_map_modalop.
Variable A B: Type.

Lemma and_tl_map :
forall (f: A->B) (P P': infseq A->Prop) (Q Q': infseq B->Prop),
(forall s, P s -> Q (map f s)) ->
(forall s, P' s -> Q' (map f s)) ->
forall (s: infseq A),
(P /\_ P') s -> (Q /\_ Q') (map f s).