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14
15 include "ground/arith/nat_succ_iter.ma".
16 include "ground/arith/nat_rplus.ma".
17
18 (* RIGHT ADDITION FOR NON-NEGATIVE INTEGERS *********************************)
19
20 (* Constructions with nsucc *************************************************)
21
22 lemma nrplus_succ_dx (p) (n): ↑(p+n) = p + ↑n.
23 #p #n @(niter_succ … psucc)
24 qed.
25
26 lemma nrplus_succ_shift (p) (n): ↑p + n = p + ↑n.
27 // qed.
28
29 lemma nrplus_unit_sn (n): ↑n = 𝟏 + n.
30 #n @(nat_ind_succ … n) -n //
31 qed.
32
33 (* Advanced constructions ***************************************************)
34
35 lemma nrplus_comm_23 (p) (n1) (n2):
36       p + n1 + n2 = p + n2 + n1.
37 #p #n1 @(nat_ind_succ … n1) -n1 //
38 qed.