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authorGravatar herbelin <herbelin@85f007b7-540e-0410-9357-904b9bb8a0f7>2008-12-26 14:25:12 +0000
committerGravatar herbelin <herbelin@85f007b7-540e-0410-9357-904b9bb8a0f7>2008-12-26 14:25:12 +0000
commit85832c4d17c205644534f6ebb5cbe7c2053f9f9b (patch)
tree1d6c4f9b9c13333cc3a512d50d880c577b4a6734 /theories/Init/Peano.v
parente4b85d5e575c684df24ad7259207a185c5d5e179 (diff)
- Optimized "auto decomp" which had a (presumably) exponential in
the number of conjunctions to split. - A few cleaning and uniformisation in auto.ml. - Removal of v62 hints already in core. git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@11715 85f007b7-540e-0410-9357-904b9bb8a0f7
Diffstat (limited to 'theories/Init/Peano.v')
-rw-r--r--theories/Init/Peano.v28
1 files changed, 14 insertions, 14 deletions
diff --git a/theories/Init/Peano.v b/theories/Init/Peano.v
index 8a5b195d1..322a25468 100644
--- a/theories/Init/Peano.v
+++ b/theories/Init/Peano.v
@@ -59,13 +59,13 @@ Proof.
rewrite Sn_eq_Sm; trivial.
Qed.
-Hint Immediate eq_add_S: core v62.
+Hint Immediate eq_add_S: core.
Theorem not_eq_S : forall n m:nat, n <> m -> S n <> S m.
Proof.
red in |- *; auto.
Qed.
-Hint Resolve not_eq_S: core v62.
+Hint Resolve not_eq_S: core.
Definition IsSucc (n:nat) : Prop :=
match n with
@@ -80,13 +80,13 @@ Proof.
unfold not; intros n H.
inversion H.
Qed.
-Hint Resolve O_S: core v62.
+Hint Resolve O_S: core.
Theorem n_Sn : forall n:nat, n <> S n.
Proof.
induction n; auto.
Qed.
-Hint Resolve n_Sn: core v62.
+Hint Resolve n_Sn: core.
(** Addition *)
@@ -105,7 +105,7 @@ Lemma plus_n_O : forall n:nat, n = n + 0.
Proof.
induction n; simpl in |- *; auto.
Qed.
-Hint Resolve plus_n_O: core v62.
+Hint Resolve plus_n_O: core.
Lemma plus_O_n : forall n:nat, 0 + n = n.
Proof.
@@ -116,7 +116,7 @@ Lemma plus_n_Sm : forall n m:nat, S (n + m) = n + S m.
Proof.
intros n m; induction n; simpl in |- *; auto.
Qed.
-Hint Resolve plus_n_Sm: core v62.
+Hint Resolve plus_n_Sm: core.
Lemma plus_Sn_m : forall n m:nat, S n + m = S (n + m).
Proof.
@@ -138,13 +138,13 @@ Fixpoint mult (n m:nat) {struct n} : nat :=
where "n * m" := (mult n m) : nat_scope.
-Hint Resolve (f_equal2 mult): core v62.
+Hint Resolve (f_equal2 mult): core.
Lemma mult_n_O : forall n:nat, 0 = n * 0.
Proof.
induction n; simpl in |- *; auto.
Qed.
-Hint Resolve mult_n_O: core v62.
+Hint Resolve mult_n_O: core.
Lemma mult_n_Sm : forall n m:nat, n * m + n = n * S m.
Proof.
@@ -152,7 +152,7 @@ Proof.
destruct H; rewrite <- plus_n_Sm; apply (f_equal S).
pattern m at 1 3 in |- *; elim m; simpl in |- *; auto.
Qed.
-Hint Resolve mult_n_Sm: core v62.
+Hint Resolve mult_n_Sm: core.
(** Standard associated names *)
@@ -179,21 +179,21 @@ Inductive le (n:nat) : nat -> Prop :=
where "n <= m" := (le n m) : nat_scope.
-Hint Constructors le: core v62.
-(*i equivalent to : "Hints Resolve le_n le_S : core v62." i*)
+Hint Constructors le: core.
+(*i equivalent to : "Hints Resolve le_n le_S : core." i*)
Definition lt (n m:nat) := S n <= m.
-Hint Unfold lt: core v62.
+Hint Unfold lt: core.
Infix "<" := lt : nat_scope.
Definition ge (n m:nat) := m <= n.
-Hint Unfold ge: core v62.
+Hint Unfold ge: core.
Infix ">=" := ge : nat_scope.
Definition gt (n m:nat) := m < n.
-Hint Unfold gt: core v62.
+Hint Unfold gt: core.
Infix ">" := gt : nat_scope.