diff options
Diffstat (limited to 'src/Util/NatUtil.v')
| -rw-r--r-- | src/Util/NatUtil.v | 5 |
1 files changed, 3 insertions, 2 deletions
diff --git a/src/Util/NatUtil.v b/src/Util/NatUtil.v index 865dc08f0..1e75b3494 100644 --- a/src/Util/NatUtil.v +++ b/src/Util/NatUtil.v @@ -1,6 +1,7 @@ Require Coq.Logic.Eqdep_dec. Require Import Coq.Numbers.Natural.Peano.NPeano Coq.omega.Omega. Require Import Coq.Classes.Morphisms. +Require Import Coq.Relations.Relation_Definitions. Require Import Coq.micromega.Lia. Import Nat. @@ -68,10 +69,10 @@ Qed. Global Instance nat_rect_Proper_nondep {P} : Proper (Logic.eq ==> pointwise_relation _ (pointwise_relation _ Logic.eq) ==> Logic.eq ==> Logic.eq) (@nat_rect (fun _ => P)). Proof. repeat intro; subst; apply (@nat_rect_Proper (fun _ => P)); eauto. Qed. -Global Instance nat_rect_Proper_nondep_gen {P} (R : relation P) : Proper (R ==> (eq ==> R ==> R) ==> Logic.eq ==> R) (@nat_rect (fun _ => P)) | 100. +Global Instance nat_rect_Proper_nondep_gen {P} (R : relation P) : Proper (R ==> (Logic.eq ==> R ==> R) ==> Logic.eq ==> R) (@nat_rect (fun _ => P)) | 100. Proof. cbv [forall_relation respectful]; intros O_case O_case' HO S_case S_case' HS n n' ?; subst n'; revert O_case O_case' HO. - induction n as [|n IHn]; cbn [nat_rect]; intros; rewrite ?IHn, ?HS; auto. + induction n as [|n IHn]; cbn [nat_rect]; intros; eauto. Qed. Lemma nat_eq_dec_S x y |