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13 (**************************************************************************)
14
15 include "ground_2/arith.ma".
16
17 (* ITEMS ********************************************************************)
18
19 (* atomic items *)
20 inductive item0: Type[0] ≝
21    | Sort: nat → item0 (* sort: starting at 0 *)
22    | LRef: nat → item0 (* reference by index: starting at 0 *)
23    | GRef: nat → item0 (* reference by position: starting at 0 *)
24 .
25
26 (* binary binding items *)
27 inductive bind2: Type[0] ≝
28   | Abbr: bind2 (* abbreviation *)
29   | Abst: bind2 (* abstraction *)
30 .
31
32 (* binary non-binding items *)
33 inductive flat2: Type[0] ≝
34   | Appl: flat2 (* application *)
35   | Cast: flat2 (* explicit type annotation *)
36 .
37
38 (* binary items *)
39 inductive item2: Type[0] ≝
40   | Bind2: bool → bind2 → item2 (* polarized binding item *)
41   | Flat2: flat2 → item2        (* non-binding item *)
42 .
43
44 (* Basic properties *********************************************************)
45
46 axiom eq_item0_dec: ∀I1,I2:item0. Decidable (I1 = I2).
47
48 (* Basic_1: was: bind_dec *)
49 axiom eq_bind2_dec: ∀I1,I2:bind2. Decidable (I1 = I2).
50
51 (* Basic_1: was: flat_dec *)
52 axiom eq_flat2_dec: ∀I1,I2:flat2. Decidable (I1 = I2).
53
54 (* Basic_1: was: kind_dec *)
55 axiom eq_item2_dec: ∀I1,I2:item2. Decidable (I1 = I2).
56
57 (* Basic_1: removed theorems 21:
58             s_S s_plus s_plus_sym s_minus minus_s_s s_le s_lt s_inj s_inc
59             s_arith0 s_arith1
60             r_S r_plus r_plus_sym r_minus r_dis s_r r_arith0 r_arith1
61             not_abbr_abst bind_dec_not
62 *)