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14
15 include "ground/arith/nat_rplus_succ.ma".
16 include "ground/arith/nat_plus.ma".
17
18 (* ADDITION FOR NON-NEGATIVE INTEGERS ***************************************)
19
20 (* Constructions with nrplus ************************************************)
21
22 lemma nrplus_inj_sn (p) (n):
23       ninj (p + n) = ninj p + n.
24 #p #n @(nat_ind_succ … n) -n //
25 #n #IH <nplus_succ_dx <IH //
26 qed.
27
28 (* Constructions with nrplus and npsucc *************************************)
29
30 lemma nrplus_npsucc_sn (m) (n):
31       npsucc (m + n) = npsucc m + n.
32 #m @(nat_ind_succ … m) -m //
33 #m #IH #n <npsucc_succ <nrplus_succ_sn //
34 qed.