proposition: Lemma format_unused_sequence_correct {cache : Cache} {S V1 T : Type} {P : CacheDecode -> Prop} {P_inv1 P_inv2 : (CacheDecode -> Prop) -> Prop} (P_inv_pf : cache_inv_Property P (fun P => P_inv1 P /\ P_inv2 P)) (monoid : Monoid T) (Source_Predicate : S -> Prop) (View_Predicate1 : V1 -> Prop) (format1 : FormatM V1 T) (format2 : FormatM S T ) (decode1 : DecodeM (V1 * T) T) (decode_1_OK : cache_inv_Property P P_inv1 -> CorrectDecoder monoid View_Predicate1 View_Predicate1 eq format1 decode1 P format1) (View_Predicate_OK : forall v, View_Predicate1 v) (decode2 : DecodeM (S * T) T) (decode2_pf : cache_inv_Property P P_inv2 -> CorrectDecoder monoid Source_Predicate Source_Predicate eq format2 decode2 P format2) : CorrectDecoder monoid Source_Predicate Source_Predicate eq (Compose_Format format1 (fun _ _ => True) ++ format2) (sequence_Decode decode1 (fun _ => decode2)) P (Compose_Format format1 (fun _ _ => True) ++ format2).
proof: Proof. eapply sequence_Compose_format_decode_correct; intros; eauto. eauto. eapply format_decode_correct_alt_Proper; eauto; try reflexivity. - unfold flip, pointwise_relation; intuition. - unfold flip, pointwise_relation, impl; intuition. - unfold flip, EquivFormat; reflexivity. - unfold flip, EquivFormat; reflexivity. Qed.
imports: Coq.ZArith.ZArith Fiat.Common Fiat.Computation.Notations Fiat.Narcissus.Common.Specs Fiat.Narcissus.Common.WordFacts Fiat.Computation.Refinements.General Fiat.Narcissus.BaseFormats