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infseq.v
@@ -22,6 +22,7 @@ Definition hd (s:infseq) : T := match s with Cons x _ => x end.
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Definition tl (s:infseq) : infseq := match s with Cons _ s => s end.
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Lemma recons : forall s, Cons (hd s) (tl s) = s.
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+Proof.
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intros s.
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(* Trick : simpl doesn't progress, you have to eat s first *)
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case s. simpl. reflexivity.
@@ -227,6 +228,7 @@ Qed.
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Lemma eventually_until_cumul :
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forall (s: infseq T) P J,
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eventually P s -> until J P s -> eventually (P /\_ until J P) s.
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intros s P J ev. induction ev as [s Ps | x s evPs induc_hyp].
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intro un. constructor 1. split; assumption.
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intro unxs. case (until_Cons _ _ _ _ unxs).
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