diff options
Diffstat (limited to 'theories/Arith/Between.v')
| -rw-r--r-- | theories/Arith/Between.v | 24 |
1 files changed, 12 insertions, 12 deletions
diff --git a/theories/Arith/Between.v b/theories/Arith/Between.v index f998e861..58d3a2b3 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. |