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4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
10 (* \ / This file is distributed under the terms of the *)
11 (* v GNU General Public License Version 2 *)
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15 include "ground/arith/pnat_lt.ma".
17 (* WELL-FOUNDED INDUCTION ***************************************************)
19 fact wf1_ind_plt_aux (A1) (f:A1→pnat) (Q:predicate …):
20 (∀p. (∀a1. f a1 < p → Q a1) → ∀a1. f a1 = p → Q a1) →
21 ∀p,a1. f a1 = p → Q a1.
22 #A1 #f #Q #H #p @(pnat_ind_lt … p) -p /3 width=3 by/
25 lemma wf1_ind_plt (A1) (f:A1→pnat) (Q:predicate …):
26 (∀p. (∀a1. f a1 < p → Q a1) → ∀a1. f a1 = p → Q a1) →
28 #A #f #Q #H #a1 @(wf1_ind_plt_aux … H) -H //