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authorGravatar filliatr <filliatr@85f007b7-540e-0410-9357-904b9bb8a0f7>1999-12-13 13:42:04 +0000
committerGravatar filliatr <filliatr@85f007b7-540e-0410-9357-904b9bb8a0f7>1999-12-13 13:42:04 +0000
commitdecb8c16274487ce3cac1e7d5de529b46b6d68e3 (patch)
tree02a41980403e4c3fbeab8259a95ea14ba1b80e65 /theories/Init/Peano.v
parent7dfacfe208a9fa5ad5f7669537c54609b4adf51e (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-xtheories/Init/Peano.v26
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.