lean2/library/logic/wf_k.lean
2014-11-21 10:03:20 -08:00

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-- Copyright (c) 2014 Microsoft Corporation. All rights reserved.
-- Released under Apache 2.0 license as described in the file LICENSE.
-- Author: Leonardo de Moura
import logic.wf data.nat.basic
namespace well_founded
-- This is an auxiliary definition that useful for generating a new "proof" for (well_founded R)
-- that allows us to use well_founded.fix and execute the definitions up to k nested recursive
-- calls without "computing" with the proofs in Hwf.
definition intro_k {A : Type} {R : A → A → Prop} (Hwf : well_founded R) (k : nat) : well_founded R :=
well_founded.intro
(nat.rec_on k
(λ n : A, well_founded.apply Hwf n)
(λ (k' : nat) (f : Πa, acc R a), (λ n : A, acc.intro n (λ y H, f y))))
end well_founded