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15 include "ground_2/ynat/ynat.ma".
17 (* NATURAL NUMBERS WITH INFINITY ********************************************)
19 (* the predecessor function *)
20 definition ypred: ynat → ynat ≝ λm. match m with
25 interpretation "ynat predecessor" 'DownArrow m = (ypred m).
27 lemma ypred_O: ↓(yinj 0) = yinj 0.
30 lemma ypred_S: ∀m:nat. ↓(↑m) = yinj m.
33 lemma ypred_Y: (↓∞) = ∞.
36 (* Inversion lemmas *********************************************************)
38 lemma ypred_inv_refl: ∀m:ynat. ↓m = m → m = 0 ∨ m = ∞.
39 * // #m #H lapply (yinj_inj … H) -H (**) (* destruct lemma needed *)
40 /4 width=1 by pred_inv_fix_sn, or_introl, eq_f/