diff --git a/theories/base.v b/theories/base.v index 82c6b8d656a965d4b4ee50219c839d7663253dcb..24ea3864c93ce7c1a9d2a049854f7cf4265d437c 100644 --- a/theories/base.v +++ b/theories/base.v @@ -862,6 +862,9 @@ Instance idem_propholds {A} (R : relation A) f : Idempotent R f → ∀ x, PropHolds (R (f x x) x). Proof. red. trivial. Qed. +Instance: ∀ `{R1 : relation A, R2 : relation B} (x : B), + Reflexive R2 → Proper (R1 ==> R2) (λ _, x). +Proof. intros A R1 B R2 x ? y1 y2; reflexivity. Qed. Instance: @PreOrder A (=). Proof. split; repeat intro; congruence. Qed. Lemma injective_iff {A B} {R : relation A} {S : relation B} (f : A → B) diff --git a/theories/numbers.v b/theories/numbers.v index f0f366a854251d021f7d362eefc8256cfbde17c5..d7d5ec961d24178f4a0d9f5bbabac13a39d149c6 100644 --- a/theories/numbers.v +++ b/theories/numbers.v @@ -11,6 +11,7 @@ Open Scope nat_scope. Coercion Z.of_nat : nat >-> Z. (** * Notations and properties of [nat] *) +Arguments minus !_ !_ /. Reserved Notation "x ≤ y ≤ z" (at level 70, y at next level). Reserved Notation "x ≤ y < z" (at level 70, y at next level). Reserved Notation "x < y < z" (at level 70, y at next level).