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-rw-r--r--theories/Init/Notations.v8
-rw-r--r--theories/Init/Peano.v3
-rw-r--r--theories/ZArith/Zbool.v4
3 files changed, 7 insertions, 8 deletions
diff --git a/theories/Init/Notations.v b/theories/Init/Notations.v
index c4780ace52..0c628298dc 100644
--- a/theories/Init/Notations.v
+++ b/theories/Init/Notations.v
@@ -68,13 +68,13 @@ Reserved Notation "{ x }" (at level 0, x at level 99).
(** Notations for sigma-types or subsets *)
Reserved Notation "{ x | P }" (at level 0, x at level 99).
-Reserved Notation "{ x | P & Q }" (at level 0, x at level 99).
+Reserved Notation "{ x | P & Q }" (at level 0, x at level 99).
Reserved Notation "{ x : A | P }" (at level 0, x at level 99).
-Reserved Notation "{ x : A | P & Q }" (at level 0, x at level 99).
+Reserved Notation "{ x : A | P & Q }" (at level 0, x at level 99).
-Reserved Notation "{ x : A & P }" (at level 0, x at level 99).
-Reserved Notation "{ x : A & P & Q }" (at level 0, x at level 99).
+Reserved Notation "{ x : A & P }" (at level 0, x at level 99).
+Reserved Notation "{ x : A & P & Q }" (at level 0, x at level 99).
Delimit Scope type_scope with type.
Delimit Scope core_scope with core.
diff --git a/theories/Init/Peano.v b/theories/Init/Peano.v
index 322a25468a..9924d8a658 100644
--- a/theories/Init/Peano.v
+++ b/theories/Init/Peano.v
@@ -77,8 +77,7 @@ Definition IsSucc (n:nat) : Prop :=
Theorem O_S : forall n:nat, 0 <> S n.
Proof.
- unfold not; intros n H.
- inversion H.
+ discriminate.
Qed.
Hint Resolve O_S: core.
diff --git a/theories/ZArith/Zbool.v b/theories/ZArith/Zbool.v
index cce0438fa6..5aab73f2e0 100644
--- a/theories/ZArith/Zbool.v
+++ b/theories/ZArith/Zbool.v
@@ -18,9 +18,9 @@ Require Import Sumbool.
Unset Boxed Definitions.
Open Local Scope Z_scope.
-(** * Boolean operations from decidabilty of order *)
+(** * Boolean operations from decidability of order *)
(** The decidability of equality and order relations over
- type [Z] give some boolean functions with the adequate specification. *)
+ type [Z] gives some boolean functions with the adequate specification. *)
Definition Z_lt_ge_bool (x y:Z) := bool_of_sumbool (Z_lt_ge_dec x y).
Definition Z_ge_lt_bool (x y:Z) := bool_of_sumbool (Z_ge_lt_dec x y).