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Factor ZRange Proper proof (#1764)
For #1761
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‎src/AbstractInterpretation/Wf.v

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@@ -25,14 +25,17 @@ Require Import Rewriter.Language.Inversion.
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Require Import Crypto.Language.InversionExtra.
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Require Import Rewriter.Language.Wf.
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Require Import Rewriter.Language.UnderLetsProofs.
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Require Import Rewriter.Util.Decidable.
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Require Import Crypto.AbstractInterpretation.AbstractInterpretation.
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Require Import Crypto.AbstractInterpretation.ZRangeCommonProofs.
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Import Coq.Lists.List.
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Import EqNotations.
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Module Compilers.
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Import Language.Compilers.
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Import UnderLets.Compilers.
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Import AbstractInterpretation.Compilers.
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Import AbstractInterpretation.ZRangeCommonProofs.Compilers.
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Import Language.Inversion.Compilers.
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Import Language.InversionExtra.Compilers.
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Import Language.Wf.Compilers.
@@ -852,39 +855,7 @@ Module Compilers.
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Global Instance abstract_interp_ident_Proper {opts : AbstractInterpretation.Options} {assume_cast_truncates : bool} {t}
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: Proper (eq ==> @abstract_domain_R t) (abstract_interp_ident assume_cast_truncates t).
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Proof using Type.
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cbv [abstract_interp_ident abstract_domain_R type.related respectful type.interp]; intros idc idc' ?; subst idc'; destruct idc;
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repeat first [ reflexivity
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| progress subst
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| progress cbn [ZRange.type.base.option.interp ZRange.type.base.interp base.interp base.base_interp Crypto.Util.Option.bind] in *
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| progress cbv [Crypto.Util.Option.bind]
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| intro
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| progress destruct_head'_prod
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| progress destruct_head'_bool
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| progress destruct_head' option
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| progress inversion_option
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| discriminate
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| solve [ eauto ]
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| apply NatUtil.nat_rect_Proper_nondep
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| apply ListUtil.list_rect_Proper
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| apply ListUtil.list_rect_arrow_Proper
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| apply ListUtil.list_case_Proper
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| apply ListUtil.pointwise_map
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| apply ListUtil.fold_right_Proper
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| apply ListUtil.update_nth_Proper
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| apply (@nat_rect_Proper_nondep_gen (_ -> _) (eq ==> eq)%signature)
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| cbn; apply (f_equal (@Some _))
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| progress cbn [ZRange.ident.option.interp]
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| progress cbv [zrange_rect]
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| apply (f_equal2 pair)
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| break_innermost_match_step
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| match goal with
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| [ H : _ |- _ ] => erewrite H by (eauto; (eassumption || reflexivity))
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| [ H : forall x y, x = y -> _ |- _ ] => specialize (fun x => H x x eq_refl)
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| [ H : forall x, ?f x = ?g x, H1 : ?f ?y = _, H2 : ?g ?y = _ |- _ ]
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=> specialize (H y); rewrite H1, H2 in H
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end ].
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Qed.
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Proof using Type. apply ZRange.ident.option.interp_Proper. Qed.
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Global Instance extract_list_state_Proper {t}
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: Proper (abstract_domain'_R _ ==> option_eq (SetoidList.eqlistA (@abstract_domain'_R t)))

‎src/AbstractInterpretation/ZRangeCommonProofs.v

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@@ -0,0 +1,63 @@
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(* Proofs shared by Wf and Proofs *)
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Require Import Coq.Classes.Morphisms.
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Require Import Coq.Relations.Relations.
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Require Import Crypto.Util.ZRange.
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Require Import Crypto.Util.Option.
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Require Import Crypto.Util.ListUtil.
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Require Import Crypto.Util.ListUtil.FoldBool.
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Require Import Crypto.Util.NatUtil.
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Require Import Crypto.Util.ZUtil.Morphisms.
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Require Import Crypto.Util.Tactics.BreakMatch.
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Require Import Crypto.Util.Tactics.DestructHead.
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Require Import Crypto.AbstractInterpretation.ZRange.
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Module Compilers.
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Import AbstractInterpretation.ZRange.Compilers.
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Export ZRange.Settings.
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Module ZRange.
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Module ident.
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Module option.
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Section interp_related.
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Context {shiftr_avoid_uint1 : shiftr_avoid_uint1_opt}
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(assume_cast_truncates : bool).
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Global Instance interp_Proper {t} : Proper (eq ==> @type.eqv t) (ZRange.ident.option.interp assume_cast_truncates).
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Proof using Type.
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intros idc idc' ?; subst idc'.
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cbv [type.related respectful type.interp]; destruct idc;
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repeat first [ reflexivity
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| progress subst
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| progress cbn [ZRange.type.base.option.interp ZRange.type.base.interp base.interp base.base_interp Crypto.Util.Option.bind] in *
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| progress cbv [Crypto.Util.Option.bind]
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| intro
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| progress destruct_head'_prod
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| progress destruct_head'_bool
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| progress destruct_head' option
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| progress inversion_option
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| discriminate
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| solve [ eauto ]
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| apply NatUtil.nat_rect_Proper_nondep
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| apply ListUtil.list_rect_Proper
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| apply ListUtil.list_rect_arrow_Proper
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| apply ListUtil.list_case_Proper
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| apply ListUtil.pointwise_map
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| apply ListUtil.fold_right_Proper
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| apply ListUtil.update_nth_Proper
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| apply (@nat_rect_Proper_nondep_gen (_ -> _) (eq ==> eq)%signature)
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| cbn; apply (f_equal (@Some _))
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| progress cbn [ZRange.ident.option.interp]
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| progress cbv [zrange_rect]
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| apply (f_equal2 pair)
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| break_innermost_match_step
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| match goal with
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| [ H : _ |- _ ] => erewrite H by (eauto; (eassumption || reflexivity))
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| [ H : forall x y, x = y -> _ |- _ ] => specialize (fun x => H x x eq_refl)
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| [ H : forall x, ?f x = ?g x, H1 : ?f ?y = _, H2 : ?g ?y = _ |- _ ]
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=> specialize (H y); rewrite H1, H2 in H
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end ].
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Qed.
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End interp_related.
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End option.
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End ident.
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End ZRange.
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End Compilers.

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