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authorGravatar letouzey <letouzey@85f007b7-540e-0410-9357-904b9bb8a0f7>2008-05-22 11:08:13 +0000
committerGravatar letouzey <letouzey@85f007b7-540e-0410-9357-904b9bb8a0f7>2008-05-22 11:08:13 +0000
commitcf73432c0e850242c7918cc348388e5cde379a8f (patch)
tree07ebc5fa4588f13416caaca476f90816beb867ae /theories/Numbers/Natural/Binary
parent313de91c9cd26e6fee94aa5bb093ae8a436fd43a (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.v8
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.