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14
15 include "ground/arith/nat_succ_tri.ma".
16 include "ground/arith/nat_lt.ma".
17
18 (* STRICT ORDER FOR NON-NEGATIVE INTEGERS ***********************************)
19
20 (* Destructions with ntri ***************************************************)
21
22 (*** tri_lt *)
23 lemma ntri_lt (A) (a1) (a2) (a3) (n1) (n2):
24       n1 < n2 → a1 = ntri A n1 n2 a1 a2 a3.
25 #A #a1 #a2 #a3 #n1 #n2 #H @(nlt_ind_alt … H) -H //
26 qed-.
27
28 (*** tri_gt *)
29 lemma ntri_gt (A) (a1) (a2) (a3) (n1) (n2):
30       n2 < n1 → a3 = ntri A n1 n2 a1 a2 a3.
31 #A #a1 #a2 #a3 #n1 #n2 #H @(nlt_ind_alt … H) -H //
32 qed-.