diff options
author | 1999-12-13 13:42:04 +0000 | |
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committer | 1999-12-13 13:42:04 +0000 | |
commit | decb8c16274487ce3cac1e7d5de529b46b6d68e3 (patch) | |
tree | 02a41980403e4c3fbeab8259a95ea14ba1b80e65 /theories/Init/Peano.v | |
parent | 7dfacfe208a9fa5ad5f7669537c54609b4adf51e (diff) |
- méthode load sur les Hints
- CAST pris en compte dans Astterm
- Coercin.lookup_path_to_sort_from protégé par un try/with
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@248 85f007b7-540e-0410-9357-904b9bb8a0f7
Diffstat (limited to 'theories/Init/Peano.v')
-rwxr-xr-x | theories/Init/Peano.v | 26 |
1 files changed, 13 insertions, 13 deletions
diff --git a/theories/Init/Peano.v b/theories/Init/Peano.v index b8bf598af..4efc6c693 100755 --- a/theories/Init/Peano.v +++ b/theories/Init/Peano.v @@ -29,8 +29,8 @@ Definition pred : nat->nat := [n:nat](Cases n of O => O | (S u) => u end). Hint eq_pred : v62 := Resolve (f_equal nat nat pred). Theorem pred_Sn : (m:nat) m=(pred (S m)). - Proof. -Auto. +Proof. + Auto. Qed. Theorem eq_add_S : (n,m:nat) (S n)=(S m) -> n=m. @@ -44,7 +44,7 @@ Hints Immediate eq_add_S : core v62. Theorem not_eq_S : (n,m:nat) ~(n=m) -> ~((S n)=(S m)). Proof. - Red; Auto. + Red; Auto. Qed. Hints Resolve not_eq_S : core v62. @@ -62,7 +62,7 @@ Hints Resolve O_S : core v62. Theorem n_Sn : (n:nat) ~(n=(S n)). Proof. - Induction n ; Auto. + Induction n ; Auto. Qed. Hints Resolve n_Sn : core v62. @@ -79,13 +79,13 @@ Hint eq_nat_binary : core := Resolve (f_equal2 nat nat). Lemma plus_n_O : (n:nat) n=(plus n O). Proof. - Induction n ; Simpl ; Auto. + Induction n ; Simpl ; Auto. Qed. Hints Resolve plus_n_O : core v62. Lemma plus_n_Sm : (n,m:nat) (S (plus n m))=(plus n (S m)). Proof. - Intros m n; Elim m; Simpl; Auto. + Intros m n; Elim m; Simpl; Auto. Qed. Hints Resolve plus_n_Sm : core v62. @@ -100,15 +100,15 @@ Hint eq_mult : core v62 := Resolve (f_equal2 nat nat nat mult). Lemma mult_n_O : (n:nat) O=(mult n O). Proof. - Induction n; Simpl; Auto. + Induction n; Simpl; Auto. Qed. Hints Resolve mult_n_O : core v62. Lemma mult_n_Sm : (n,m:nat) (plus (mult n m) n)=(mult n (S m)). Proof. - Intros; Elim n; Simpl; Auto. - Intros p H; Case H; Elim plus_n_Sm; Apply (f_equal nat nat S). - Pattern 1 3 m; Elim m; Simpl; Auto. + Intros; Elim n; Simpl; Auto. + Intros p H; Case H; Elim plus_n_Sm; Apply (f_equal nat nat S). + Pattern 1 3 m; Elim m; Simpl; Auto. Qed. Hints Resolve mult_n_Sm : core v62. @@ -141,7 +141,7 @@ Hints Unfold gt : core v62. Theorem nat_case : (n:nat)(P:nat->Prop)(P O)->((m:nat)(P (S m)))->(P n). Proof. - Induction n ; Auto. + Induction n ; Auto. Qed. (**********************************************************) @@ -153,6 +153,6 @@ Theorem nat_double_ind : (R:nat->nat->Prop) -> ((n,m:nat)(R n m)->(R (S n) (S m))) -> (n,m:nat)(R n m). Proof. - Induction n; Auto. - Induction m; Auto. + Induction n; Auto. + Induction m; Auto. Qed. |