diff options
| author |  Andres Erbsen <andreser@mit.edu> | 2016-10-10 14:03:41 -0400 |
|---|---|---|
| committer | Andres Erbsen <andreser@mit.edu> | 2016-10-10 14:08:45 -0400 |
| commit | f519be9e626aea5a0ea8605dcb6748f2c05bb52d (patch) | |
| tree | ea693c2b7800864d7c6a4e4855ec532a937f5fcf /src/Util/Decidable.v | |
| parent | 9315c846b7fe474ee85fd2674bdc8141e3f5e63a (diff) | |
Decidable: add [Z] and [nat] inequalities
Diffstat (limited to 'src/Util/Decidable.v')
| -rw-r--r-- | src/Util/Decidable.v | 19 |
1 files changed, 15 insertions, 4 deletions
diff --git a/src/Util/Decidable.v b/src/Util/Decidable.v index 6030ae819..a6954663b 100644 --- a/src/Util/Decidable.v +++ b/src/Util/Decidable.v @@ -5,7 +5,7 @@ Require Import Crypto.Util.FixCoqMistakes. Require Import Crypto.Util.Sigma. Require Import Crypto.Util.HProp. Require Import Crypto.Util.Equality. -Require Import Coq.ZArith.BinInt. +Require Import Coq.ZArith.BinInt Coq.ZArith.ZArith_dec. Require Import Coq.NArith.BinNat. Local Open Scope type_scope. @@ -96,9 +96,20 @@ Global Instance dec_eq_list {A} `{DecidableRel (@eq A)} : DecidableRel (@eq (lis Global Instance dec_eq_sum {A B} `{DecidableRel (@eq A), DecidableRel (@eq B)} : DecidableRel (@eq (A + B)) | 10. exact _. Defined. Global Instance dec_eq_sigT_hprop {A P} `{DecidableRel (@eq A), forall a : A, IsHProp (P a)} : DecidableRel (@eq (@sigT A P)) | 10. exact _. Defined. Global Instance dec_eq_sig_hprop {A} {P : A -> Prop} `{DecidableRel (@eq A), forall a : A, IsHProp (P a)} : DecidableRel (@eq (@sig A P)) | 10. exact _. Defined. + Global Instance dec_eq_nat : DecidableRel (@eq nat) | 10. exact _. Defined. +Global Instance dec_le_nat : DecidableRel le := Compare_dec.le_dec. +Global Instance dec_lt_nat : DecidableRel lt := Compare_dec.lt_dec. +Global Instance dec_ge_nat : DecidableRel ge := Compare_dec.ge_dec. +Global Instance dec_gt_nat : DecidableRel gt := Compare_dec.gt_dec. + Global Instance dec_eq_N : DecidableRel (@eq N) | 10 := N.eq_dec. + Global Instance dec_eq_Z : DecidableRel (@eq Z) | 10 := Z.eq_dec. +Global Instance dec_lt_Z : DecidableRel BinInt.Z.lt := ZArith_dec.Z_lt_dec. +Global Instance dec_le_Z : DecidableRel BinInt.Z.le := ZArith_dec.Z_le_dec. +Global Instance dec_gt_Z : DecidableRel BinInt.Z.gt := ZArith_dec.Z_gt_dec. +Global Instance dec_ge_Z : DecidableRel BinInt.Z.ge := ZArith_dec.Z_ge_dec. Lemma not_not P {d:Decidable P} : not (not P) <-> P. Proof. destruct (dec P); intuition. Qed. @@ -132,11 +143,11 @@ Proof. eauto using dec_of_semidec. Defined. Lemma dec_bool : forall {P} {Pdec:Decidable P}, (if dec P then true else false) = true -> P. Proof. intros. destruct dec; solve [ auto | discriminate ]. Qed. -Ltac vm_decide := apply dec_bool; vm_compute; reflexivity. -Ltac lazy_decide := apply dec_bool; lazy; reflexivity. - Ltac vm_decide_no_check := apply dec_bool; vm_cast_no_check (eq_refl true). Ltac lazy_decide_no_check := apply dec_bool; exact_no_check (eq_refl true). +Ltac vm_decide := abstract vm_decide_no_check. +Ltac lazy_decide := abstract lazy_decide_no_check. + (** For dubious compatibility with [eauto using]. *) Hint Extern 2 (Decidable _) => progress unfold Decidable : typeclass_instances core. |