diff options
Diffstat (limited to 'theories')
35 files changed, 155 insertions, 161 deletions
diff --git a/theories/Arith/Between.v b/theories/Arith/Between.v index f998e8619..58d3a2b38 100644 --- a/theories/Arith/Between.v +++ b/theories/Arith/Between.v @@ -20,20 +20,20 @@ Section Between. | bet_emp : between k k | bet_S : forall l, between k l -> P l -> between k (S l). - Hint Constructors between: arith v62. + Hint Constructors between: arith. Lemma bet_eq : forall k l, l = k -> between k l. Proof. induction 1; auto with arith. Qed. - Hint Resolve bet_eq: arith v62. + Hint Resolve bet_eq: arith. Lemma between_le : forall k l, between k l -> k <= l. Proof. induction 1; auto with arith. Qed. - Hint Immediate between_le: arith v62. + Hint Immediate between_le: arith. Lemma between_Sk_l : forall k l, between k l -> S k <= l -> between (S k) l. Proof. @@ -41,7 +41,7 @@ Section Between. intros; absurd (S k <= k); auto with arith. destruct H; auto with arith. Qed. - Hint Resolve between_Sk_l: arith v62. + Hint Resolve between_Sk_l: arith. Lemma between_restr : forall k l (m:nat), k <= l -> l <= m -> between k m -> between l m. @@ -53,7 +53,7 @@ Section Between. | exists_S : forall l, exists_between k l -> exists_between k (S l) | exists_le : forall l, k <= l -> Q l -> exists_between k (S l). - Hint Constructors exists_between: arith v62. + Hint Constructors exists_between: arith. Lemma exists_le_S : forall k l, exists_between k l -> S k <= l. Proof. @@ -62,13 +62,13 @@ Section Between. Lemma exists_lt : forall k l, exists_between k l -> k < l. Proof exists_le_S. - Hint Immediate exists_le_S exists_lt: arith v62. + Hint Immediate exists_le_S exists_lt: arith. Lemma exists_S_le : forall k l, exists_between k (S l) -> k <= l. Proof. intros; apply le_S_n; auto with arith. Qed. - Hint Immediate exists_S_le: arith v62. + Hint Immediate exists_S_le: arith. Definition in_int p q r := p <= r /\ r < q. @@ -76,7 +76,7 @@ Section Between. Proof. red; auto with arith. Qed. - Hint Resolve in_int_intro: arith v62. + Hint Resolve in_int_intro: arith. Lemma in_int_lt : forall p q r, in_int p q r -> p < q. Proof. @@ -95,13 +95,13 @@ Section Between. Proof. induction 1; auto with arith. Qed. - Hint Resolve in_int_S: arith v62. + Hint Resolve in_int_S: arith. Lemma in_int_Sp_q : forall p q r, in_int (S p) q r -> in_int p q r. Proof. induction 1; auto with arith. Qed. - Hint Immediate in_int_Sp_q: arith v62. + Hint Immediate in_int_Sp_q: arith. Lemma between_in_int : forall k l, between k l -> forall r, in_int k l r -> P r. @@ -183,5 +183,5 @@ Section Between. End Between. Hint Resolve nth_O bet_S bet_emp bet_eq between_Sk_l exists_S exists_le - in_int_S in_int_intro: arith v62. -Hint Immediate in_int_Sp_q exists_le_S exists_S_le: arith v62. + in_int_S in_int_intro: arith. +Hint Immediate in_int_Sp_q exists_le_S exists_S_le: arith. diff --git a/theories/Arith/EqNat.v b/theories/Arith/EqNat.v index 206fc0ab5..f998c19fc 100644 --- a/theories/Arith/EqNat.v +++ b/theories/Arith/EqNat.v @@ -25,7 +25,7 @@ Theorem eq_nat_refl n : eq_nat n n. Proof. induction n; simpl; auto. Qed. -Hint Resolve eq_nat_refl: arith v62. +Hint Resolve eq_nat_refl: arith. (** [eq] restricted to [nat] and [eq_nat] are equivalent *) @@ -46,7 +46,7 @@ Proof. apply eq_nat_is_eq. Qed. -Hint Immediate eq_eq_nat eq_nat_eq: arith v62. +Hint Immediate eq_eq_nat eq_nat_eq: arith. Theorem eq_nat_elim : forall n (P:nat -> Prop), P n -> forall m, eq_nat n m -> P m. diff --git a/theories/Arith/Gt.v b/theories/Arith/Gt.v index dfd576946..67c94fdf6 100644 --- a/theories/Arith/Gt.v +++ b/theories/Arith/Gt.v @@ -133,14 +133,14 @@ Qed. (** * Hints *) -Hint Resolve gt_Sn_O gt_Sn_n gt_n_S : arith v62. -Hint Immediate gt_S_n gt_pred : arith v62. -Hint Resolve gt_irrefl gt_asym : arith v62. -Hint Resolve le_not_gt gt_not_le : arith v62. -Hint Immediate le_S_gt gt_S_le : arith v62. -Hint Resolve gt_le_S le_gt_S : arith v62. -Hint Resolve gt_trans_S le_gt_trans gt_le_trans: arith v62. -Hint Resolve plus_gt_compat_l: arith v62. +Hint Resolve gt_Sn_O gt_Sn_n gt_n_S : arith. +Hint Immediate gt_S_n gt_pred : arith. +Hint Resolve gt_irrefl gt_asym : arith. +Hint Resolve le_not_gt gt_not_le : arith. +Hint Immediate le_S_gt gt_S_le : arith. +Hint Resolve gt_le_S le_gt_S : arith. +Hint Resolve gt_trans_S le_gt_trans gt_le_trans: arith. +Hint Resolve plus_gt_compat_l: arith. (* begin hide *) Notation gt_O_eq := gt_0_eq (only parsing). diff --git a/theories/Arith/Le.v b/theories/Arith/Le.v index ceb91187b..0fbcec572 100644 --- a/theories/Arith/Le.v +++ b/theories/Arith/Le.v @@ -30,8 +30,8 @@ Notation le_refl := Nat.le_refl (compat "8.4"). Notation le_trans := Nat.le_trans (compat "8.4"). Notation le_antisym := Nat.le_antisymm (compat "8.4"). -Hint Resolve le_trans: arith v62. -Hint Immediate le_antisym: arith v62. +Hint Resolve le_trans: arith. +Hint Immediate le_antisym: arith. (** * Properties of [le] w.r.t 0 *) @@ -59,16 +59,16 @@ Notation le_Sn_n := Nat.nle_succ_diag_l (compat "8.4"). (* ~ S n <= n *) Theorem le_Sn_le : forall n m, S n <= m -> n <= m. Proof Nat.lt_le_incl. -Hint Resolve le_0_n le_Sn_0: arith v62. -Hint Resolve le_n_S le_n_Sn le_Sn_n : arith v62. -Hint Immediate le_n_0_eq le_Sn_le le_S_n : arith v62. +Hint Resolve le_0_n le_Sn_0: arith. +Hint Resolve le_n_S le_n_Sn le_Sn_n : arith. +Hint Immediate le_n_0_eq le_Sn_le le_S_n : arith. (** * Properties of [le] w.r.t predecessor *) Notation le_pred_n := Nat.le_pred_l (compat "8.4"). (* pred n <= n *) Notation le_pred := Nat.pred_le_mono (compat "8.4"). (* n<=m -> pred n <= pred m *) -Hint Resolve le_pred_n: arith v62. +Hint Resolve le_pred_n: arith. (** * A different elimination principle for the order on natural numbers *) diff --git a/theories/Arith/Lt.v b/theories/Arith/Lt.v index f824ee6fb..bfc2b91a9 100644 --- a/theories/Arith/Lt.v +++ b/theories/Arith/Lt.v @@ -25,7 +25,7 @@ Local Open Scope nat_scope. Notation lt_irrefl := Nat.lt_irrefl (compat "8.4"). (* ~ x < x *) -Hint Resolve lt_irrefl: arith v62. +Hint Resolve lt_irrefl: arith. (** * Relationship between [le] and [lt] *) @@ -44,9 +44,9 @@ Proof. apply Nat.lt_succ_r. Qed. -Hint Immediate lt_le_S: arith v62. -Hint Immediate lt_n_Sm_le: arith v62. -Hint Immediate le_lt_n_Sm: arith v62. +Hint Immediate lt_le_S: arith. +Hint Immediate lt_n_Sm_le: arith. +Hint Immediate le_lt_n_Sm: arith. Theorem le_not_lt n m : n <= m -> ~ m < n. Proof. @@ -58,7 +58,7 @@ Proof. apply Nat.lt_nge. Qed. -Hint Immediate le_not_lt lt_not_le: arith v62. +Hint Immediate le_not_lt lt_not_le: arith. (** * Asymmetry *) @@ -79,8 +79,8 @@ Proof. intros. now apply Nat.neq_sym, Nat.neq_0_lt_0. Qed. -Hint Resolve lt_0_Sn lt_n_0 : arith v62. -Hint Immediate neq_0_lt lt_0_neq: arith v62. +Hint Resolve lt_0_Sn lt_n_0 : arith. +Hint Immediate neq_0_lt lt_0_neq: arith. (** * Order and successor *) @@ -97,8 +97,8 @@ Proof. apply Nat.succ_lt_mono. Qed. -Hint Resolve lt_n_Sn lt_S lt_n_S : arith v62. -Hint Immediate lt_S_n : arith v62. +Hint Resolve lt_n_Sn lt_S lt_n_S : arith. +Hint Immediate lt_S_n : arith. (** * Predecessor *) @@ -117,8 +117,8 @@ Proof. intros. now apply Nat.lt_pred_l, Nat.neq_0_lt_0. Qed. -Hint Immediate lt_pred: arith v62. -Hint Resolve lt_pred_n_n: arith v62. +Hint Immediate lt_pred: arith. +Hint Resolve lt_pred_n_n: arith. (** * Transitivity properties *) @@ -126,7 +126,7 @@ Notation lt_trans := Nat.lt_trans (compat "8.4"). Notation lt_le_trans := Nat.lt_le_trans (compat "8.4"). Notation le_lt_trans := Nat.le_lt_trans (compat "8.4"). -Hint Resolve lt_trans lt_le_trans le_lt_trans: arith v62. +Hint Resolve lt_trans lt_le_trans le_lt_trans: arith. (** * Large = strict or equal *) @@ -139,7 +139,7 @@ Qed. Notation lt_le_weak := Nat.lt_le_incl (compat "8.4"). -Hint Immediate lt_le_weak: arith v62. +Hint Immediate lt_le_weak: arith. (** * Dichotomy *) diff --git a/theories/Arith/Max.v b/theories/Arith/Max.v index 65534b2e3..49152549a 100644 --- a/theories/Arith/Max.v +++ b/theories/Arith/Max.v @@ -42,7 +42,7 @@ Notation max_SS := Nat.succ_max_distr (only parsing). (* end hide *) Hint Resolve - Nat.max_l Nat.max_r Nat.le_max_l Nat.le_max_r : arith v62. + Nat.max_l Nat.max_r Nat.le_max_l Nat.le_max_r : arith. Hint Resolve - Nat.min_l Nat.min_r Nat.le_min_l Nat.le_min_r : arith v62. + Nat.min_l Nat.min_r Nat.le_min_l Nat.le_min_r : arith. diff --git a/theories/Arith/Minus.v b/theories/Arith/Minus.v index bc3a318cf..1fc8f7907 100644 --- a/theories/Arith/Minus.v +++ b/theories/Arith/Minus.v @@ -107,13 +107,13 @@ Qed. (** * Hints *) -Hint Resolve minus_n_O: arith v62. -Hint Resolve minus_Sn_m: arith v62. -Hint Resolve minus_diag_reverse: arith v62. -Hint Resolve minus_plus_simpl_l_reverse: arith v62. -Hint Immediate plus_minus: arith v62. -Hint Resolve minus_plus: arith v62. -Hint Resolve le_plus_minus: arith v62. -Hint Resolve le_plus_minus_r: arith v62. -Hint Resolve lt_minus: arith v62. -Hint Immediate lt_O_minus_lt: arith v62. +Hint Resolve minus_n_O: arith. +Hint Resolve minus_Sn_m: arith. +Hint Resolve minus_diag_reverse: arith. +Hint Resolve minus_plus_simpl_l_reverse: arith. +Hint Immediate plus_minus: arith. +Hint Resolve minus_plus: arith. +Hint Resolve le_plus_minus: arith. +Hint Resolve le_plus_minus_r: arith. +Hint Resolve lt_minus: arith. +Hint Immediate lt_O_minus_lt: arith. diff --git a/theories/Arith/Mult.v b/theories/Arith/Mult.v index 965812432..a173efc10 100644 --- a/theories/Arith/Mult.v +++ b/theories/Arith/Mult.v @@ -31,13 +31,13 @@ Notation mult_0_r := Nat.mul_0_r (compat "8.4"). (* n * 0 = 0 *) Notation mult_1_l := Nat.mul_1_l (compat "8.4"). (* 1 * n = n *) Notation mult_1_r := Nat.mul_1_r (compat "8.4"). (* n * 1 = n *) -Hint Resolve mult_1_l mult_1_r: arith v62. +Hint Resolve mult_1_l mult_1_r: arith. (** ** Commutativity *) Notation mult_comm := Nat.mul_comm (compat "8.4"). (* n * m = m * n *) -Hint Resolve mult_comm: arith v62. +Hint Resolve mult_comm: arith. (** ** Distributivity *) @@ -53,9 +53,9 @@ Notation mult_minus_distr_r := Notation mult_minus_distr_l := Nat.mul_sub_distr_l (compat "8.4"). (* n*(m-p) = n*m - n*p *) -Hint Resolve mult_plus_distr_r: arith v62. -Hint Resolve mult_minus_distr_r: arith v62. -Hint Resolve mult_minus_distr_l: arith v62. +Hint Resolve mult_plus_distr_r: arith. +Hint Resolve mult_minus_distr_r: arith. +Hint Resolve mult_minus_distr_l: arith. (** ** Associativity *) @@ -66,8 +66,8 @@ Proof. symmetry. apply Nat.mul_assoc. Qed. -Hint Resolve mult_assoc_reverse: arith v62. -Hint Resolve mult_assoc: arith v62. +Hint Resolve mult_assoc_reverse: arith. +Hint Resolve mult_assoc: arith. (** ** Inversion lemmas *) @@ -92,7 +92,7 @@ Lemma mult_O_le n m : m = 0 \/ n <= m * n. Proof. destruct m; [left|right]; simpl; trivial using Nat.le_add_r. Qed. -Hint Resolve mult_O_le: arith v62. +Hint Resolve mult_O_le: arith. Lemma mult_le_compat_l n m p : n <= m -> p * n <= p * m. Proof. diff --git a/theories/Arith/Plus.v b/theories/Arith/Plus.v index 3b823da6f..600e5e518 100644 --- a/theories/Arith/Plus.v +++ b/theories/Arith/Plus.v @@ -177,12 +177,12 @@ Proof (succ_plus_discr n 3). (** * Compatibility Hints *) -Hint Immediate plus_comm : arith v62. -Hint Resolve plus_assoc plus_assoc_reverse : arith v62. -Hint Resolve plus_le_compat_l plus_le_compat_r : arith v62. -Hint Resolve le_plus_l le_plus_r le_plus_trans : arith v62. -Hint Immediate lt_plus_trans : arith v62. -Hint Resolve plus_lt_compat_l plus_lt_compat_r : arith v62. +Hint Immediate plus_comm : arith. +Hint Resolve plus_assoc plus_assoc_reverse : arith. +Hint Resolve plus_le_compat_l plus_le_compat_r : arith. +Hint Resolve le_plus_l le_plus_r le_plus_trans : arith. +Hint Immediate lt_plus_trans : arith. +Hint Resolve plus_lt_compat_l plus_lt_compat_r : arith. (** For compatibility, we "Require" the same files as before *) diff --git a/theories/Bool/Bool.v b/theories/Bool/Bool.v index 721ab6932..06096c66a 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). diff --git a/theories/Bool/IfProp.v b/theories/Bool/IfProp.v index 11f3d1d6f..4257b4bc1 100644 --- a/theories/Bool/IfProp.v +++ b/theories/Bool/IfProp.v @@ -12,7 +12,7 @@ Inductive IfProp (A B:Prop) : bool -> Prop := | Iftrue : A -> IfProp A B true | Iffalse : B -> IfProp A B false. -Hint Resolve Iftrue Iffalse: bool v62. +Hint Resolve Iftrue Iffalse: bool. Lemma Iftrue_inv : forall (A B:Prop) (b:bool), IfProp A B b -> b = true -> A. destruct 1; intros; auto with bool. diff --git a/theories/Init/Logic_Type.v b/theories/Init/Logic_Type.v index 4a5f2ad69..4536dfc0f 100644 --- a/theories/Init/Logic_Type.v +++ b/theories/Init/Logic_Type.v @@ -64,7 +64,7 @@ Definition identity_rect_r : intros A x P H y H0; case identity_sym with (1 := H0); trivial. Defined. -Hint Immediate identity_sym not_identity_sym: core v62. +Hint Immediate identity_sym not_identity_sym: core. Notation refl_id := identity_refl (compat "8.3"). Notation sym_id := identity_sym (compat "8.3"). diff --git a/theories/Init/Peano.v b/theories/Init/Peano.v index 3749baf61..6c4a63501 100644 --- a/theories/Init/Peano.v +++ b/theories/Init/Peano.v @@ -33,7 +33,6 @@ Open Scope nat_scope. Definition eq_S := f_equal S. Definition f_equal_nat := f_equal (A:=nat). -Hint Resolve eq_S: v62. Hint Resolve f_equal_nat: core. (** The predecessor function *) @@ -41,7 +40,6 @@ Hint Resolve f_equal_nat: core. Notation pred := Nat.pred (compat "8.4"). Definition f_equal_pred := f_equal pred. -Hint Resolve f_equal_pred: v62. Theorem pred_Sn : forall n:nat, n = pred (S n). Proof. @@ -85,7 +83,6 @@ Notation plus := Nat.add (compat "8.4"). Infix "+" := Nat.add : nat_scope. Definition f_equal2_plus := f_equal2 plus. -Hint Resolve f_equal2_plus: v62. Definition f_equal2_nat := f_equal2 (A1:=nat) (A2:=nat). Hint Resolve f_equal2_nat: core. diff --git a/theories/Init/Specif.v b/theories/Init/Specif.v index d1038186e..9fc00e80c 100644 --- a/theories/Init/Specif.v +++ b/theories/Init/Specif.v @@ -299,7 +299,7 @@ Proof. apply (h2 h1). Defined. -Hint Resolve left right inleft inright: core v62. +Hint Resolve left right inleft inright: core. Hint Resolve exist exist2 existT existT2: core. (* Compatibility *) diff --git a/theories/Lists/List.v b/theories/Lists/List.v index bf21ffb47..30f1dec22 100644 --- a/theories/Lists/List.v +++ b/theories/Lists/List.v @@ -340,11 +340,11 @@ Section Facts. End Facts. -Hint Resolve app_assoc app_assoc_reverse: datatypes v62. -Hint Resolve app_comm_cons app_cons_not_nil: datatypes v62. -Hint Immediate app_eq_nil: datatypes v62. -Hint Resolve app_eq_unit app_inj_tail: datatypes v62. -Hint Resolve in_eq in_cons in_inv in_nil in_app_or in_or_app: datatypes v62. +Hint Resolve app_assoc app_assoc_reverse: datatypes. +Hint Resolve app_comm_cons app_cons_not_nil: datatypes. +Hint Immediate app_eq_nil: datatypes. +Hint Resolve app_eq_unit app_inj_tail: datatypes. +Hint Resolve in_eq in_cons in_inv in_nil in_app_or in_or_app: datatypes. @@ -1544,7 +1544,7 @@ Section length_order. End length_order. Hint Resolve lel_refl lel_cons_cons lel_cons lel_nil lel_nil nil_cons: - datatypes v62. + datatypes. (******************************) @@ -1613,7 +1613,7 @@ Section SetIncl. End SetIncl. Hint Resolve incl_refl incl_tl incl_tran incl_appl incl_appr incl_cons - incl_app: datatypes v62. + incl_app: datatypes. (**************************************) @@ -2365,7 +2365,7 @@ Notation rev_acc := rev_append (only parsing). Notation rev_acc_rev := rev_append_rev (only parsing). Notation AllS := Forall (only parsing). (* was formerly in TheoryList *) -Hint Resolve app_nil_end : datatypes v62. +Hint Resolve app_nil_end : datatypes. (* end hide *) Section Repeat. diff --git a/theories/Lists/Streams.v b/theories/Lists/Streams.v index 7ec3d2503..1c302b22f 100644 --- a/theories/Lists/Streams.v +++ b/theories/Lists/Streams.v @@ -51,7 +51,7 @@ Lemma tl_nth_tl : Proof. simple induction n; simpl; auto. Qed. -Hint Resolve tl_nth_tl: datatypes v62. +Hint Resolve tl_nth_tl: datatypes. Lemma Str_nth_tl_plus : forall (n m:nat) (s:Stream), diff --git a/theories/Logic/Eqdep.v b/theories/Logic/Eqdep.v index f3a2783e1..5ef86b8e7 100644 --- a/theories/Logic/Eqdep.v +++ b/theories/Logic/Eqdep.v @@ -33,5 +33,5 @@ Export EqdepTheory. (** Exported hints *) -Hint Resolve eq_dep_eq: eqdep v62. +Hint Resolve eq_dep_eq: eqdep. Hint Resolve inj_pair2 inj_pairT2: eqdep. diff --git a/theories/Reals/RIneq.v b/theories/Reals/RIneq.v index f26bac2bb..379fee6f4 100644 --- a/theories/Reals/RIneq.v +++ b/theories/Reals/RIneq.v @@ -389,7 +389,7 @@ Lemma Rplus_ne : forall r, r + 0 = r /\ 0 + r = r. Proof. split; ring. Qed. -Hint Resolve Rplus_ne: real v62. +Hint Resolve Rplus_ne: real. (**********) @@ -425,7 +425,6 @@ Proof. apply (f_equal (fun v => v + r)). Qed. -(*i Old i*)Hint Resolve Rplus_eq_compat_l: v62. (**********) Lemma Rplus_eq_reg_l : forall r r1 r2, r + r1 = r + r2 -> r1 = r2. @@ -501,21 +500,21 @@ Lemma Rmult_0_r : forall r, r * 0 = 0. Proof. intro; ring. Qed. -Hint Resolve Rmult_0_r: real v62. +Hint Resolve Rmult_0_r: real. (**********) Lemma Rmult_0_l : forall r, 0 * r = 0. Proof. intro; ring. Qed. -Hint Resolve Rmult_0_l: real v62. +Hint Resolve Rmult_0_l: real. (**********) Lemma Rmult_ne : forall r, r * 1 = r /\ 1 * r = r. Proof. intro; split; ring. Qed. -Hint Resolve Rmult_ne: real v62. +Hint Resolve Rmult_ne: real. (**********) Lemma Rmult_1_r : forall r, r * 1 = r. @@ -530,7 +529,6 @@ Proof. auto with real. Qed. -(*i Old i*)Hint Resolve Rmult_eq_compat_l: v62. Lemma Rmult_eq_compat_r : forall r r1 r2, r1 = r2 -> r1 * r = r2 * r. Proof. @@ -646,7 +644,7 @@ Lemma Ropp_0 : -0 = 0. Proof. ring. Qed. -Hint Resolve Ropp_0: real v62. +Hint Resolve Ropp_0: real. (**********) Lemma Ropp_eq_0_compat : forall r, r = 0 -> - r = 0. diff --git a/theories/Reals/Raxioms.v b/theories/Reals/Raxioms.v index 9d55e4e63..9fbda92a2 100644 --- a/theories/Reals/Raxioms.v +++ b/theories/Reals/Raxioms.v @@ -32,7 +32,7 @@ Hint Resolve Rplus_assoc: real. (**********) Axiom Rplus_opp_r : forall r:R, r + - r = 0. -Hint Resolve Rplus_opp_r: real v62. +Hint Resolve Rplus_opp_r: real. (**********) Axiom Rplus_0_l : forall r:R, 0 + r = r. @@ -44,11 +44,11 @@ Hint Resolve Rplus_0_l: real. (**********) Axiom Rmult_comm : forall r1 r2:R, r1 * r2 = r2 * r1. -Hint Resolve Rmult_comm: real v62. +Hint Resolve Rmult_comm: real. (**********) Axiom Rmult_assoc : forall r1 r2 r3:R, r1 * r2 * r3 = r1 * (r2 * r3). -Hint Resolve Rmult_assoc: real v62. +Hint Resolve Rmult_assoc: real. (**********) Axiom Rinv_l : forall r:R, r <> 0 -> / r * r = 1. @@ -69,7 +69,7 @@ Hint Resolve R1_neq_R0: real. (**********) Axiom Rmult_plus_distr_l : forall r1 r2 r3:R, r1 * (r2 + r3) = r1 * r2 + r1 * r3. -Hint Resolve Rmult_plus_distr_l: real v62. +Hint Resolve Rmult_plus_distr_l: real. (*********************************************************) (** * Order axioms *) diff --git a/theories/Relations/Relation_Definitions.v b/theories/Relations/Relation_Definitions.v index b6005b9d1..9c98879ce 100644 --- a/theories/Relations/Relation_Definitions.v +++ b/theories/Relations/Relation_Definitions.v @@ -66,10 +66,10 @@ Section Relation_Definition. End Relation_Definition. -Hint Unfold reflexive transitive antisymmetric symmetric: sets v62. +Hint Unfold reflexive transitive antisymmetric symmetric: sets. Hint Resolve Build_preorder Build_order Build_equivalence Build_PER preord_refl preord_trans ord_refl ord_trans ord_antisym equiv_refl - equiv_trans equiv_sym per_sym per_trans: sets v62. + equiv_trans equiv_sym per_sym per_trans: sets. -Hint Unfold inclusion same_relation commut: sets v62. +Hint Unfold inclusion same_relation commut: sets. diff --git a/theories/Relations/Relation_Operators.v b/theories/Relations/Relation_Operators.v index ffd682d62..88239475c 100644 --- a/theories/Relations/Relation_Operators.v +++ b/theories/Relations/Relation_Operators.v @@ -226,9 +226,9 @@ Section Lexicographic_Exponentiation. End Lexicographic_Exponentiation. -Hint Unfold transp union: sets v62. -Hint Resolve t_step rt_step rt_refl rst_step rst_refl: sets v62. -Hint Immediate rst_sym: sets v62. +Hint Unfold transp union: sets. +Hint Resolve t_step rt_step rt_refl rst_step rst_refl: sets. +Hint Immediate rst_sym: sets. (* begin hide *) (* Compatibility *) diff --git a/theories/Sets/Classical_sets.v b/theories/Sets/Classical_sets.v index 8a4bb9f42..837437a22 100644 --- a/theories/Sets/Classical_sets.v +++ b/theories/Sets/Classical_sets.v @@ -122,4 +122,4 @@ Section Ensembles_classical. End Ensembles_classical. Hint Resolve Strict_super_set_contains_new_element Subtract_intro - not_SIncl_empty: sets v62. + not_SIncl_empty: sets. diff --git a/theories/Sets/Constructive_sets.v b/theories/Sets/Constructive_sets.v index 8d2344f93..6291248eb 100644 --- a/theories/Sets/Constructive_sets.v +++ b/theories/Sets/Constructive_sets.v @@ -141,4 +141,4 @@ End Ensembles_facts. Hint Resolve Singleton_inv Singleton_intro Add_intro1 Add_intro2 Intersection_inv Couple_inv Setminus_intro Strict_Included_intro Strict_Included_strict Noone_in_empty Inhabited_not_empty Add_not_Empty - not_Empty_Add Inhabited_add Included_Empty: sets v62. + not_Empty_Add Inhabited_add Included_Empty: sets. diff --git a/theories/Sets/Ensembles.v b/theories/Sets/Ensembles.v index 8f579214a..0fefb354b 100644 --- a/theories/Sets/Ensembles.v +++ b/theories/Sets/Ensembles.v @@ -90,9 +90,8 @@ Section Ensembles. End Ensembles. -Hint Unfold In Included Same_set Strict_Included Add Setminus Subtract: sets - v62. +Hint Unfold In Included Same_set Strict_Included Add Setminus Subtract: sets. Hint Resolve Union_introl Union_intror Intersection_intro In_singleton Couple_l Couple_r Triple_l Triple_m Triple_r Disjoint_intro - Extensionality_Ensembles: sets v62. + Extensionality_Ensembles: sets. diff --git a/theories/Sets/Finite_sets.v b/theories/Sets/Finite_sets.v index f38dd6fdf..edbc1efec 100644 --- a/theories/Sets/Finite_sets.v +++ b/theories/Sets/Finite_sets.v @@ -43,8 +43,8 @@ Section Ensembles_finis. End Ensembles_finis. -Hint Resolve Empty_is_finite Union_is_finite: sets v62. -Hint Resolve card_empty card_add: sets v62. +Hint Resolve Empty_is_finite Union_is_finite: sets. +Hint Resolve card_empty card_add: sets. Require Import Constructive_sets. diff --git a/theories/Sets/Image.v b/theories/Sets/Image.v index 34ea857d1..e74ef41e4 100644 --- a/theories/Sets/Image.v +++ b/theories/Sets/Image.v @@ -200,4 +200,4 @@ Section Image. End Image. -Hint Resolve Im_def image_empty finite_image: sets v62. +Hint Resolve Im_def image_empty finite_image: sets. diff --git a/theories/Sets/Multiset.v b/theories/Sets/Multiset.v index ec38b8923..42d0c76dc 100644 --- a/theories/Sets/Multiset.v +++ b/theories/Sets/Multiset.v @@ -187,7 +187,7 @@ End multiset_defs. Unset Implicit Arguments. -Hint Unfold meq multiplicity: v62 datatypes. +Hint Unfold meq multiplicity: datatypes. Hint Resolve munion_empty_right munion_comm munion_ass meq_left meq_right - munion_empty_left: v62 datatypes. -Hint Immediate meq_sym: v62 datatypes. + munion_empty_left: datatypes. +Hint Immediate meq_sym: datatypes. diff --git a/theories/Sets/Partial_Order.v b/theories/Sets/Partial_Order.v index 3610ebce6..335fec5b0 100644 --- a/theories/Sets/Partial_Order.v +++ b/theories/Sets/Partial_Order.v @@ -51,8 +51,8 @@ Section Partial_orders. End Partial_orders. -Hint Unfold Carrier_of Rel_of Strict_Rel_of: sets v62. -Hint Resolve Definition_of_covers: sets v62. +Hint Unfold Carrier_of Rel_of Strict_Rel_of: sets. +Hint Resolve Definition_of_covers: sets. Section Partial_order_facts. diff --git a/theories/Sets/Powerset.v b/theories/Sets/Powerset.v index d636e0468..7c2435da0 100644 --- a/theories/Sets/Powerset.v +++ b/theories/Sets/Powerset.v @@ -175,14 +175,14 @@ Qed. End The_power_set_partial_order. -Hint Resolve Empty_set_minimal: sets v62. -Hint Resolve Power_set_Inhabited: sets v62. -Hint Resolve Inclusion_is_an_order: sets v62. -Hint Resolve Inclusion_is_transitive: sets v62. -Hint Resolve Union_minimal: sets v62. -Hint Resolve Union_increases_l: sets v62. -Hint Resolve Union_increases_r: sets v62. -Hint Resolve Intersection_decreases_l: sets v62. -Hint Resolve Intersection_decreases_r: sets v62. -Hint Resolve Empty_set_is_Bottom: sets v62. -Hint Resolve Strict_inclusion_is_transitive: sets v62. +Hint Resolve Empty_set_minimal: sets. +Hint Resolve Power_set_Inhabited: sets. +Hint Resolve Inclusion_is_an_order: sets. +Hint Resolve Inclusion_is_transitive: sets. +Hint Resolve Union_minimal: sets. +Hint Resolve Union_increases_l: sets. +Hint Resolve Union_increases_r: sets. +Hint Resolve Intersection_decreases_l: sets. +Hint Resolve Intersection_decreases_r: sets. +Hint Resolve Empty_set_is_Bottom: sets. +Hint Resolve Strict_inclusion_is_transitive: sets. diff --git a/theories/Sets/Powerset_Classical_facts.v b/theories/Sets/Powerset_Classical_facts.v index 09c90506b..e802beac9 100644 --- a/theories/Sets/Powerset_Classical_facts.v +++ b/theories/Sets/Powerset_Classical_facts.v @@ -90,7 +90,7 @@ Section Sets_as_an_algebra. apply Subtract_intro; auto with sets. red; intro H'1; apply H'; rewrite H'1; auto with sets. Qed. - Hint Resolve incl_soustr_add_r: sets v62. + Hint Resolve incl_soustr_add_r: sets. Lemma add_soustr_2 : forall (X:Ensemble U) (x:U), @@ -328,9 +328,9 @@ Section Sets_as_an_algebra. End Sets_as_an_algebra. -Hint Resolve incl_soustr_in: sets v62. -Hint Resolve incl_soustr: sets v62. -Hint Resolve incl_soustr_add_l: sets v62. -Hint Resolve incl_soustr_add_r: sets v62. -Hint Resolve add_soustr_1 add_soustr_2: sets v62. -Hint Resolve add_soustr_xy: sets v62. +Hint Resolve incl_soustr_in: sets. +Hint Resolve incl_soustr: sets. +Hint Resolve incl_soustr_add_l: sets. +Hint Resolve incl_soustr_add_r: sets. +Hint Resolve add_soustr_1 add_soustr_2: sets. +Hint Resolve add_soustr_xy: sets. diff --git a/theories/Sets/Powerset_facts.v b/theories/Sets/Powerset_facts.v index 63e84199d..e9696a1ca 100644 --- a/theories/Sets/Powerset_facts.v +++ b/theories/Sets/Powerset_facts.v @@ -254,5 +254,5 @@ Section Sets_as_an_algebra. End Sets_as_an_algebra. Hint Resolve Empty_set_zero Empty_set_zero' Union_associative Union_add - singlx incl_add: sets v62. + singlx incl_add: sets. diff --git a/theories/Sets/Relations_1.v b/theories/Sets/Relations_1.v index de96fa560..45fb8134c 100644 --- a/theories/Sets/Relations_1.v +++ b/theories/Sets/Relations_1.v @@ -60,6 +60,6 @@ Section Relations_1. End Relations_1. Hint Unfold Reflexive Transitive Antisymmetric Symmetric contains - same_relation: sets v62. + same_relation: sets. Hint Resolve Definition_of_preorder Definition_of_order - Definition_of_equivalence Definition_of_PER: sets v62. + Definition_of_equivalence Definition_of_PER: sets. diff --git a/theories/Sets/Relations_2.v b/theories/Sets/Relations_2.v index f1026e31a..1e0b83fe5 100644 --- a/theories/Sets/Relations_2.v +++ b/theories/Sets/Relations_2.v @@ -48,7 +48,7 @@ Definition Strongly_confluent : Prop := End Relations_2. -Hint Resolve Rstar_0: sets v62. -Hint Resolve Rstar1_0: sets v62. -Hint Resolve Rstar1_1: sets v62. -Hint Resolve Rplus_0: sets v62. +Hint Resolve Rstar_0: sets. +Hint Resolve Rstar1_0: sets. +Hint Resolve Rstar1_1: sets. +Hint Resolve Rplus_0: sets. diff --git a/theories/Sets/Relations_3.v b/theories/Sets/Relations_3.v index 92b299885..c05b5ee76 100644 --- a/theories/Sets/Relations_3.v +++ b/theories/Sets/Relations_3.v @@ -51,10 +51,10 @@ Section Relations_3. Definition Noetherian : Prop := forall x:U, noetherian x. End Relations_3. -Hint Unfold coherent: sets v62. -Hint Unfold locally_confluent: sets v62. -Hint Unfold confluent: sets v62. -Hint Unfold Confluent: sets v62. -Hint Resolve definition_of_noetherian: sets v62. -Hint Unfold Noetherian: sets v62. +Hint Unfold coherent: sets. +Hint Unfold locally_confluent: sets. +Hint Unfold confluent: sets. +Hint Unfold Confluent: sets. +Hint Resolve definition_of_noetherian: sets. +Hint Unfold Noetherian: sets. diff --git a/theories/ZArith/Zwf.v b/theories/ZArith/Zwf.v index 1ac00bddd..90754af3b 100644 --- a/theories/ZArith/Zwf.v +++ b/theories/ZArith/Zwf.v @@ -56,7 +56,7 @@ Section wf_proof. End wf_proof. -Hint Resolve Zwf_well_founded: datatypes v62. +Hint Resolve Zwf_well_founded: datatypes. (** We also define the other family of relations: @@ -88,4 +88,4 @@ Section wf_proof_up. End wf_proof_up. -Hint Resolve Zwf_up_well_founded: datatypes v62. +Hint Resolve Zwf_up_well_founded: datatypes. |