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14
15 include "ground/arith/nat_tri.ma".
16 include "ground/arith/nat_succ.ma".
17
18 (* SUCCESSOR FOR NON-NEGATIVE INTEGERS **************************************)
19
20 (* Constructions with ntri **************************************************)
21
22 lemma ntri_zero_succ (A) (a1) (a2) (a3) (n):
23       a1 = ntri A (𝟎) (↑n) a1 a2 a3.
24 #A #a1 #a2 #a3 * //
25 qed.
26
27 lemma ntri_succ_zero (A) (a1) (a2) (a3) (n):
28       a3 = ntri A (↑n) (𝟎) a1 a2 a3.
29 #A #a1 #a2 #a3 * //
30 qed.
31
32 lemma ntri_succ_bi (A) (a1) (a2) (a3) (n1) (n2):
33       ntri A (n1) (n2) a1 a2 a3 = ntri A (↑n1) (↑n2) a1 a2 a3.
34 #A #a1 #a2 #a3 * [| #p1 ] * //
35 qed.