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15 include "ground/arith/nat_rplus_pplus.ma".
16 include "ground/arith/nat_plus_rplus.ma".
18 (* ADDITION FOR NON-NEGATIVE INTEGERS ***************************************)
20 lemma nplus_inj_bi (p) (q):
21 ninj (pplus p q) = nplus (ninj p) (ninj q).
24 lemma nplus_pnpred_sn (p) (q):
25 pnpred (p + q) = nplus (pnpred p) (ninj q).
27 <pplus_comm >nplus_comm >nrplus_pnpred_dx //