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15 include "ground/arith/nat_pred_succ.ma".
16 include "ground/arith/nat_lt.ma".
18 (* STRICT ORDER FOR NON-NEGATIVE INTEGERS ***********************************)
20 (* Constructions with npred *************************************************)
22 lemma nlt_zero_sn (m): m = ↑↓m → 𝟎 < m.
25 (* Inversions with npred ****************************************************)
28 lemma nlt_inv_zero_sn (m): 𝟎 < m → m = ↑↓m.
29 #m @(nat_ind … m) -m //
30 #H elim (nlt_inv_refl … H)