diff options
Diffstat (limited to 'theories/ZArith/Zabs.v')
| -rw-r--r-- | theories/ZArith/Zabs.v | 15 |
1 files changed, 3 insertions, 12 deletions
diff --git a/theories/ZArith/Zabs.v b/theories/ZArith/Zabs.v index 36eb41104..ba454c327 100644 --- a/theories/ZArith/Zabs.v +++ b/theories/ZArith/Zabs.v @@ -23,21 +23,12 @@ Open Local Scope Z_scope. (**********************************************************************) (** * Properties of absolute value *) -Lemma Zabs_eq : forall n:Z, 0 <= n -> Zabs n = n. -Proof. - intro x; destruct x; auto with arith. - compute in |- *; intros; absurd (Gt = Gt); trivial with arith. -Qed. - -Lemma Zabs_non_eq : forall n:Z, n <= 0 -> Zabs n = - n. -Proof. - intro x; destruct x; auto with arith. - compute in |- *; intros; absurd (Gt = Gt); trivial with arith. -Qed. +Notation Zabs_eq := Zabs_eq (only parsing). (* 0 <= n -> Zabs n = n *) +Notation Zabs_non_eq := Zabs_non_eq (only parsing). (* n <= 0 -> Zabs n = -n *) Theorem Zabs_Zopp : forall n:Z, Zabs (- n) = Zabs n. Proof. - intros z; case z; simpl in |- *; auto. + intros z; case z; simpl; auto. Qed. (** * Proving a property of the absolute value by cases *) |