diff --git a/theories/numbers.v b/theories/numbers.v index 65b9621e9377f9720ca2ba31bcf158a03ac2c302..023f91f47a095d6d05788d66de444377b09f8b76 100644 --- a/theories/numbers.v +++ b/theories/numbers.v @@ -28,6 +28,10 @@ Notation "x ≤ y ≤ z ≤ z'" := (x ≤ y ∧ y ≤ z ∧ z ≤ z')%nat : nat_ Notation "(≤)" := le (only parsing) : nat_scope. Notation "(<)" := lt (only parsing) : nat_scope. +Infix "≥" := ge : nat_scope. +Notation "(≥)" := ge (only parsing) : nat_scope. +Notation "(>)" := gt (only parsing) : nat_scope. + Infix "`div`" := Nat.div (at level 35) : nat_scope. Infix "`mod`" := Nat.modulo (at level 35) : nat_scope. @@ -104,6 +108,10 @@ Notation "(<)" := Pos.lt (only parsing) : positive_scope. Notation "(~0)" := xO (only parsing) : positive_scope. Notation "(~1)" := xI (only parsing) : positive_scope. +Infix "≥" := Pos.ge : positive_scope. +Notation "(≥)" := Pos.ge (only parsing) : positive_scope. +Notation "(>)" := Pos.gt (only parsing) : positive_scope. + Arguments Pos.of_nat _ : simpl never. Instance positive_eq_dec: ∀ x y : positive, Decision (x = y) := Pos.eq_dec. Instance positive_inhabited: Inhabited positive := populate 1. @@ -179,6 +187,11 @@ Notation "x < y ≤ z" := (x < y ∧ y ≤ z)%N : N_scope. Notation "x ≤ y ≤ z ≤ z'" := (x ≤ y ∧ y ≤ z ∧ z ≤ z')%N : N_scope. Notation "(≤)" := N.le (only parsing) : N_scope. Notation "(<)" := N.lt (only parsing) : N_scope. + +Infix "≥" := N.ge : N_scope. +Notation "(≥)" := N.ge (only parsing) : N_scope. +Notation "(>)" := N.gt (only parsing) : N_scope. + Infix "`div`" := N.div (at level 35) : N_scope. Infix "`mod`" := N.modulo (at level 35) : N_scope. @@ -213,6 +226,10 @@ Notation "x ≤ y ≤ z ≤ z'" := (x ≤ y ∧ y ≤ z ∧ z ≤ z') : Z_scope. Notation "(≤)" := Z.le (only parsing) : Z_scope. Notation "(<)" := Z.lt (only parsing) : Z_scope. +Infix "≥" := Z.ge : Z_scope. +Notation "(≥)" := Z.ge (only parsing) : Z_scope. +Notation "(>)" := Z.gt (only parsing) : Z_scope. + Infix "`div`" := Z.div (at level 35) : Z_scope. Infix "`mod`" := Z.modulo (at level 35) : Z_scope. Infix "`quot`" := Z.quot (at level 35) : Z_scope. @@ -328,6 +345,10 @@ Notation "x ≤ y ≤ z ≤ z'" := (x ≤ y ∧ y ≤ z ∧ z ≤ z') : Qc_scope Notation "(≤)" := Qcle (only parsing) : Qc_scope. Notation "(<)" := Qclt (only parsing) : Qc_scope. +Infix "≥" := Qcge : Qc_scope. +Notation "(≥)" := Qcge (only parsing) : Qc_scope. +Notation "(>)" := Qcgt (only parsing) : Qc_scope. + Hint Extern 1 (_ ≤ _) => reflexivity || discriminate. Arguments Qred _ : simpl never.