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4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
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15 include "ground_2/notation/functions/predecessor_1.ma".
16 include "ground_2/lib/arith.ma".
17 include "ground_2/ynat/ynat.ma".
19 (* NATURAL NUMBERS WITH INFINITY ********************************************)
21 (* the predecessor function *)
22 definition ypred: ynat → ynat ≝ λm. match m with
27 interpretation "ynat predecessor" 'Predecessor m = (ypred m).
29 (* Properties ***************************************************************)
31 lemma ypred_inj_rew: ∀m:nat. ⫰m = pred m.
34 (* Inversion lemmas *********************************************************)
36 lemma ypred_inv_refl: ∀m. ⫰m = m → m = 0 ∨ m = ∞.
37 * // #m #H lapply (yinj_inj … H) -H (**) (* destruct lemma needed *)
38 /4 width=1 by pred_inv_refl, or_introl, eq_f/