diff options
author | letouzey <letouzey@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2008-05-22 11:08:13 +0000 |
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committer | letouzey <letouzey@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2008-05-22 11:08:13 +0000 |
commit | cf73432c0e850242c7918cc348388e5cde379a8f (patch) | |
tree | 07ebc5fa4588f13416caaca476f90816beb867ae /theories/Numbers/Natural/Binary | |
parent | 313de91c9cd26e6fee94aa5bb093ae8a436fd43a (diff) |
switch theories/Numbers from Set to Type (both the abstract and the bignum part).
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@10964 85f007b7-540e-0410-9357-904b9bb8a0f7
Diffstat (limited to 'theories/Numbers/Natural/Binary')
-rw-r--r-- | theories/Numbers/Natural/Binary/NBinDefs.v | 8 |
1 files changed, 4 insertions, 4 deletions
diff --git a/theories/Numbers/Natural/Binary/NBinDefs.v b/theories/Numbers/Natural/Binary/NBinDefs.v index c2af66724..170dfa42f 100644 --- a/theories/Numbers/Natural/Binary/NBinDefs.v +++ b/theories/Numbers/Natural/Binary/NBinDefs.v @@ -197,7 +197,7 @@ Qed. End NZOrdAxiomsMod. -Definition recursion (A : Set) (a : A) (f : N -> A -> A) (n : N) := +Definition recursion (A : Type) (a : A) (f : N -> A -> A) (n : N) := Nrect (fun _ => A) a f n. Implicit Arguments recursion [A]. @@ -207,7 +207,7 @@ reflexivity. Qed. Theorem recursion_wd : -forall (A : Set) (Aeq : relation A), +forall (A : Type) (Aeq : relation A), forall a a' : A, Aeq a a' -> forall f f' : N -> A -> A, fun2_eq NZeq Aeq Aeq f f' -> forall x x' : N, x = x' -> @@ -224,13 +224,13 @@ now apply Eff'; [| apply IH]. Qed. Theorem recursion_0 : - forall (A : Set) (a : A) (f : N -> A -> A), recursion a f N0 = a. + forall (A : Type) (a : A) (f : N -> A -> A), recursion a f N0 = a. Proof. intros A a f; unfold recursion; now rewrite Nrect_base. Qed. Theorem recursion_succ : - forall (A : Set) (Aeq : relation A) (a : A) (f : N -> A -> A), + forall (A : Type) (Aeq : relation A) (a : A) (f : N -> A -> A), Aeq a a -> fun2_wd NZeq Aeq Aeq f -> forall n : N, Aeq (recursion a f (Nsucc n)) (f n (recursion a f n)). Proof. |