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4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
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15 include "ground_2/notation.ma".
16 include "ground_2/xoa_props.ma".
17 include "ground_2/ynat/ynat.ma".
19 (* INFINITARY NATURAL NUMBERS ***********************************************)
21 (* "is_zero" predicate *)
22 definition yzero: predicate ynat ≝ λx. match x with
27 (* Inversion lemmas *********************************************************)
29 lemma discr_YS_YO: ∀n. ⫯n = 0 → ⊥.
30 #n #H change with (yzero (⫯n))
34 lemma discr_YO_YS: ∀n. ynat_of_nat 0 = ⫯n → ⊥. (**) (* explicit coercion *)
35 /2 width=2 by discr_YS_YO/ qed-.