diff options
Diffstat (limited to 'theories/Bool/Bool.v')
| -rw-r--r-- | theories/Bool/Bool.v | 30 |
1 files changed, 15 insertions, 15 deletions
diff --git a/theories/Bool/Bool.v b/theories/Bool/Bool.v index 721ab693..06096c66 100644 --- a/theories/Bool/Bool.v +++ b/theories/Bool/Bool.v @@ -39,13 +39,13 @@ Lemma diff_true_false : true <> false. Proof. discriminate. Qed. -Hint Resolve diff_true_false : bool v62. +Hint Resolve diff_true_false : bool. Lemma diff_false_true : false <> true. Proof. discriminate. Qed. -Hint Resolve diff_false_true : bool v62. +Hint Resolve diff_false_true : bool. Hint Extern 1 (false <> true) => exact diff_false_true. Lemma eq_true_false_abs : forall b:bool, b = true -> b = false -> False. @@ -82,7 +82,7 @@ Definition leb (b1 b2:bool) := | true => b2 = true | false => True end. -Hint Unfold leb: bool v62. +Hint Unfold leb: bool. Lemma leb_implb : forall b1 b2, leb b1 b2 <-> implb b1 b2 = true. Proof. @@ -242,14 +242,14 @@ Lemma orb_true_intro : Proof. intros; apply orb_true_iff; trivial. Qed. -Hint Resolve orb_true_intro: bool v62. +Hint Resolve orb_true_intro: bool. Lemma orb_false_intro : forall b1 b2:bool, b1 = false -> b2 = false -> b1 || b2 = false. Proof. intros. subst. reflexivity. Qed. -Hint Resolve orb_false_intro: bool v62. +Hint Resolve orb_false_intro: bool. Lemma orb_false_elim : forall b1 b2:bool, b1 || b2 = false -> b1 = false /\ b2 = false. @@ -268,7 +268,7 @@ Lemma orb_true_r : forall b:bool, b || true = true. Proof. destr_bool. Qed. -Hint Resolve orb_true_r: bool v62. +Hint Resolve orb_true_r: bool. Lemma orb_true_l : forall b:bool, true || b = true. Proof. @@ -284,13 +284,13 @@ Lemma orb_false_r : forall b:bool, b || false = b. Proof. destr_bool. Qed. -Hint Resolve orb_false_r: bool v62. +Hint Resolve orb_false_r: bool. Lemma orb_false_l : forall b:bool, false || b = b. Proof. destr_bool. Qed. -Hint Resolve orb_false_l: bool v62. +Hint Resolve orb_false_l: bool. Notation orb_b_false := orb_false_r (only parsing). Notation orb_false_b := orb_false_l (only parsing). @@ -301,7 +301,7 @@ Lemma orb_negb_r : forall b:bool, b || negb b = true. Proof. destr_bool. Qed. -Hint Resolve orb_negb_r: bool v62. +Hint Resolve orb_negb_r: bool. Notation orb_neg_b := orb_negb_r (only parsing). @@ -318,7 +318,7 @@ Lemma orb_assoc : forall b1 b2 b3:bool, b1 || (b2 || b3) = b1 || b2 || b3. Proof. destr_bool. Qed. -Hint Resolve orb_comm orb_assoc: bool v62. +Hint Resolve orb_comm orb_assoc: bool. (*******************************) (** * Properties of [andb] *) @@ -392,7 +392,7 @@ Lemma andb_false_elim : Proof. destruct b1; simpl; auto. Defined. -Hint Resolve andb_false_elim: bool v62. +Hint Resolve andb_false_elim: bool. (** Complementation *) @@ -400,7 +400,7 @@ Lemma andb_negb_r : forall b:bool, b && negb b = false. Proof. destr_bool. Qed. -Hint Resolve andb_negb_r: bool v62. +Hint Resolve andb_negb_r: bool. Notation andb_neg_b := andb_negb_r (only parsing). @@ -418,7 +418,7 @@ Proof. destr_bool. Qed. -Hint Resolve andb_comm andb_assoc: bool v62. +Hint Resolve andb_comm andb_assoc: bool. (*******************************************) (** * Properties mixing [andb] and [orb] *) @@ -688,7 +688,7 @@ Lemma andb_prop_intro : Proof. destr_bool; tauto. Qed. -Hint Resolve andb_prop_intro: bool v62. +Hint Resolve andb_prop_intro: bool. Notation andb_true_intro2 := (fun b1 b2 H1 H2 => andb_prop_intro b1 b2 (conj H1 H2)) @@ -699,7 +699,7 @@ Lemma andb_prop_elim : Proof. destr_bool; auto. Qed. -Hint Resolve andb_prop_elim: bool v62. +Hint Resolve andb_prop_elim: bool. Notation andb_prop2 := andb_prop_elim (only parsing). |