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15 include "ground/arith/nat_lt.ma".
17 (* WELL-FOUNDED INDUCTION ***************************************************)
19 fact wf2_ind_nlt_aux (A1) (A2) (f:A1→A2→nat) (Q:relation2 …):
20 (∀n. (∀a1,a2. f a1 a2 < n → Q a1 a2) → ∀a1,a2. f a1 a2 = n → Q a1 a2) →
21 ∀n,a1,a2. f a1 a2 = n → Q a1 a2.
22 #A1 #A2 #f #Q #H #n @(nat_ind_lt … n) -n /3 width=3 by/
26 lemma wf2_ind_nlt (A1) (A2) (f:A1→A2→nat) (Q:relation2 …):
27 (∀n. (∀a1,a2. f a1 a2 < n → Q a1 a2) → ∀a1,a2. f a1 a2 = n → Q a1 a2) →
29 #A1 #A2 #f #Q #H #a1 #a2 @(wf2_ind_nlt_aux … H) -H //