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4 (* ||A|| A project by Andrea Asperti *)
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7 (* ||T|| The HELM team. *)
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15 include "ground/arith/nat_pred_succ.ma".
16 include "ground/arith/nat_le.ma".
18 (* NON-NEGATIVE INTEGERS ****************************************************)
20 (* Basic constructions with pred ********************************************)
23 lemma nle_pred_sn_refl (m): ↓m ≤ m.
27 (*** monotonic_pred *)
28 lemma nle_pred_bi (m) (n): m ≤ n → ↓m ≤ ↓n.
30 /2 width=3 by nle_trans/