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authorGravatar herbelin <herbelin@85f007b7-540e-0410-9357-904b9bb8a0f7>2006-01-23 09:07:54 +0000
committerGravatar herbelin <herbelin@85f007b7-540e-0410-9357-904b9bb8a0f7>2006-01-23 09:07:54 +0000
commit526057e6daf4a9c0eb7b931386fd1cc350c8c210 (patch)
tree521ddf0b10a3019f8297892c202be8b3518f1ebc /test-suite/success/RecTutorial.v
parent493c92e5445b033e0c25142d04336349b3a67628 (diff)
Répercussion mise à jour de Pierre Casteran vis à vis du changement de statut du paramètre de Acc
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@7921 85f007b7-540e-0410-9357-904b9bb8a0f7
Diffstat (limited to 'test-suite/success/RecTutorial.v')
-rw-r--r--test-suite/success/RecTutorial.v17
1 files changed, 8 insertions, 9 deletions
diff --git a/test-suite/success/RecTutorial.v b/test-suite/success/RecTutorial.v
index 7d3d6730f..d79b85df1 100644
--- a/test-suite/success/RecTutorial.v
+++ b/test-suite/success/RecTutorial.v
@@ -769,7 +769,7 @@ Eval simpl in even_test.
Eval simpl in (fun x : nat => even_test x).
-
+Eval simpl in (fun x : nat => plus 5 x).
Eval simpl in (fun x : nat => even_test (plus 5 x)).
Eval simpl in (fun x : nat => even_test (plus x 5)).
@@ -778,11 +778,11 @@ Eval simpl in (fun x : nat => even_test (plus x 5)).
Section Principle_of_Induction.
Variable P : nat -> Prop.
Hypothesis base_case : P 0.
-Hypothesis inductive_hyp : forall n:nat, P n -> P (S n).
+Hypothesis inductive_step : forall n:nat, P n -> P (S n).
Fixpoint nat_ind (n:nat) : (P n) :=
match n return P n with
| 0 => base_case
- | S m => inductive_hyp m (nat_ind m)
+ | S m => inductive_step m (nat_ind m)
end.
End Principle_of_Induction.
@@ -802,12 +802,12 @@ Section Principle_of_Double_Induction.
Variable P : nat -> nat ->Prop.
Hypothesis base_case1 : forall x:nat, P 0 x.
Hypothesis base_case2 : forall x:nat, P (S x) 0.
-Hypothesis inductive_hyp : forall n m:nat, P n m -> P (S n) (S m).
+Hypothesis inductive_step : forall n m:nat, P n m -> P (S n) (S m).
Fixpoint nat_double_ind (n m:nat){struct n} : P n m :=
match n, m return P n m with
| 0 , x => base_case1 x
| (S x), 0 => base_case2 x
- | (S x), (S y) => inductive_hyp x y (nat_double_ind x y)
+ | (S x), (S y) => inductive_step x y (nat_double_ind x y)
end.
End Principle_of_Double_Induction.
@@ -815,12 +815,12 @@ Section Principle_of_Double_Recursion.
Variable P : nat -> nat -> Set.
Hypothesis base_case1 : forall x:nat, P 0 x.
Hypothesis base_case2 : forall x:nat, P (S x) 0.
-Hypothesis inductive_hyp : forall n m:nat, P n m -> P (S n) (S m).
+Hypothesis inductive_step : forall n m:nat, P n m -> P (S n) (S m).
Fixpoint nat_double_rec (n m:nat){struct n} : P n m :=
match n, m return P n m with
| 0 , x => base_case1 x
| (S x), 0 => base_case2 x
- | (S x), (S y) => inductive_hyp x y (nat_double_rec x y)
+ | (S x), (S y) => inductive_step x y (nat_double_rec x y)
end.
End Principle_of_Double_Recursion.
@@ -912,7 +912,7 @@ Definition minus_decrease : forall x y:nat, Acc lt x ->
Acc lt (x-y).
Proof.
intros x y H; case H.
- intros z Hz posz posy.
+ intros Hz posz posy.
apply Hz; apply minus_smaller_positive; assumption.
Defined.
@@ -1227,4 +1227,3 @@ Qed.
-