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definition of equivalence for local environments,
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14
15 include "arithmetics/nat.ma".
16 include "ground_2/notation/constructors/infinity_0.ma".
17
18 (* NATURAL NUMBERS WITH INFINITY ********************************************)
19
20 (* the type of natural numbers with infinity *)
21 inductive ynat: Type[0] ≝
22 | yinj: nat → ynat
23 | Y   : ynat
24 .
25
26 coercion yinj.
27
28 interpretation "ynat infinity" 'Infinity = Y.
29
30 (* Inversion lemmas *********************************************************)
31
32 lemma yinj_inj: ∀m,n. yinj m = yinj n → m = n.
33 #m #n #H destruct //
34 qed-.