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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 *)
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15 include "ground/arith/ynat_lt_le.ma".
17 (* WELL-FOUNDED INDUCTION ***************************************************)
19 (*** ynat_f_ind_aux *)
20 fact wf1_ind_ylt_aux (A1) (f:A1→ynat) (Q:predicate …):
21 (∀y. (∀a1. f a1 < y → Q a1) → ∀a1. f a1 = y → Q a1) →
22 ∀y,a1. f a1 = y → Q a1.
23 #A1 #f #Q #H #y @(ynat_ind_lt … y) -y /3 width=3 by/
27 lemma wf1_ind_ylt (A1) (f:A1→ynat) (Q:predicate …):
28 (∀y. (∀a1. f a1 < y → Q a1) → ∀a1. f a1 = y → Q a1) →
30 #A #f #Q #H #a1 @(wf1_ind_ylt_aux … H) -H //