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Diffstat (limited to 'contrib/subtac/FixSub.v')
-rw-r--r-- | contrib/subtac/FixSub.v | 24 |
1 files changed, 24 insertions, 0 deletions
diff --git a/contrib/subtac/FixSub.v b/contrib/subtac/FixSub.v index bbf722db..ded069bf 100644 --- a/contrib/subtac/FixSub.v +++ b/contrib/subtac/FixSub.v @@ -20,3 +20,27 @@ Definition Fix_sub (x : A) := Fix_F_sub x (Rwf x). End FixPoint. End Well_founded. + +Require Import Wf_nat. +Require Import Lt. + +Section Well_founded_measure. +Variable A : Set. +Variable f : A -> nat. +Definition R := fun x y => f x < f y. + +Section FixPoint. + +Variable P : A -> Set. + +Variable F_sub : forall x:A, (forall y: { y : A | f y < f x }, P (proj1_sig y)) -> P x. + +Fixpoint Fix_measure_F_sub (x : A) (r : Acc lt (f x)) {struct r} : P x := + F_sub x (fun y: { y : A | f y < f x} => Fix_measure_F_sub (proj1_sig y) + (Acc_inv r (f (proj1_sig y)) (proj2_sig y))). + +Definition Fix_measure_sub (x : A) := Fix_measure_F_sub x (lt_wf (f x)). + +End FixPoint. + +End Well_founded_measure. |