diff options
Diffstat (limited to 'theories/Init/Wf.v')
| -rw-r--r-- | theories/Init/Wf.v | 12 |
1 files changed, 6 insertions, 6 deletions
diff --git a/theories/Init/Wf.v b/theories/Init/Wf.v index 2d35a4b23..f1baf71a7 100644 --- a/theories/Init/Wf.v +++ b/theories/Init/Wf.v @@ -65,7 +65,7 @@ Section Well_founded. exact (fun P:A -> Prop => well_founded_induction_type P). Defined. -(** Well-founded fixpoints *) +(** Well-founded fixpoints *) Section FixPoint. @@ -80,13 +80,13 @@ Section Well_founded. Lemma Fix_F_eq : forall (x:A) (r:Acc x), F (fun (y:A) (p:R y x) => Fix_F (x:=y) (Acc_inv r p)) = Fix_F (x:=x) r. - Proof. + Proof. destruct r using Acc_inv_dep; auto. Qed. Definition Fix (x:A) := Fix_F (Rwf x). - (** Proof that [well_founded_induction] satisfies the fixpoint equation. + (** Proof that [well_founded_induction] satisfies the fixpoint equation. It requires an extra property of the functional *) Hypothesis @@ -111,7 +111,7 @@ Section Well_founded. End FixPoint. -End Well_founded. +End Well_founded. (** Well-founded fixpoints over pairs *) @@ -120,7 +120,7 @@ Section Well_founded_2. Variables A B : Type. Variable R : A * B -> A * B -> Prop. - Variable P : A -> B -> Type. + Variable P : A -> B -> Type. Section FixPoint_2. @@ -129,7 +129,7 @@ Section Well_founded_2. forall (x:A) (x':B), (forall (y:A) (y':B), R (y, y') (x, x') -> P y y') -> P x x'. - Fixpoint Fix_F_2 (x:A) (x':B) (a:Acc R (x, x')) {struct a} : + Fixpoint Fix_F_2 (x:A) (x':B) (a:Acc R (x, x')) {struct a} : P x x' := F (fun (y:A) (y':B) (h:R (y, y') (x, x')) => |