matita/matita/contribs/lambdadelta/ground/arith/wf1_ind_plt.ma

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  14
  15 include "ground/arith/pnat_lt.ma".
  16
  17 (* WELL-FOUNDED INDUCTION ***************************************************)
  18
  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/
  23 qed-.
  24
  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) →
  27       ∀a1. Q a1.
  28 #A #f #Q #H #a1 @(wf1_ind_plt_aux … H) -H //
  29 qed-.