matita/matita/contribs/lambdadelta/ground/arith/wf1_ind_ylt.ma

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  14
  15 include "ground/arith/ynat_lt_le.ma".
  16
  17 (* WELL-FOUNDED INDUCTION ***************************************************)
  18
  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/
  24 qed-.
  25
  26 (*** ynat_f_ind *)
  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) →
  29       ∀a1. Q a1.
  30 #A #f #Q #H #a1 @(wf1_ind_ylt_aux … H) -H //
  31 qed-.