(* Specifications: *)
Lemma weak_until_until_or_always : forall (J P : infseq T -> Prop) (s : infseq T), weak_until J P s -> until J P s \/ always J s.
Lemma not_eventually_not_always : forall (P : infseq T -> Prop) (s : infseq T), ~ eventually (~_ P) s -> always P s.
Lemma not_always_eventually_not : forall (P : infseq T -> Prop) (s : infseq T), ~ always P s -> eventually (~_ P) s.
Lemma not_until_release : forall (J P : infseq T -> Prop) (s : infseq T), ~ until (~_ J) (~_ P) s -> release J P s.
Lemma not_release_until : forall (J P : infseq T -> Prop) (s : infseq T), ~ release (~_ J) (~_ P) s -> until J P s.
Lemma not_inf_often_continuously_not : forall (P : infseq T -> Prop) (s : infseq T), ~ inf_often P s -> continuously (~_ P) s.
Lemma not_continously_inf_often_not : forall (P : infseq T -> Prop) (s : infseq T), ~ continuously P s -> inf_often (~_ P) s.
Lemma not_tl_and_tl_or_tl : forall (P Q : infseq T -> Prop) (s : infseq T), (~_ (P /\_ Q)) s -> ((~_ P) \/_ (~_ Q)) s.