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14
15 include "ground_2/arith.ma".
16 include "basic_2/notation.ma".
17
18 (* ITEMS ********************************************************************)
19
20 (* atomic items *)
21 inductive item0: Type[0] ≝
22    | Sort: nat → item0 (* sort: starting at 0 *)
23    | LRef: nat → item0 (* reference by index: starting at 0 *)
24    | GRef: nat → item0 (* reference by position: starting at 0 *)
25 .
26
27 (* binary binding items *)
28 inductive bind2: Type[0] ≝
29   | Abbr: bind2 (* abbreviation *)
30   | Abst: bind2 (* abstraction *)
31 .
32
33 (* binary non-binding items *)
34 inductive flat2: Type[0] ≝
35   | Appl: flat2 (* application *)
36   | Cast: flat2 (* explicit type annotation *)
37 .
38
39 (* binary items *)
40 inductive item2: Type[0] ≝
41   | Bind2: bind2 → item2 (* binding item *)
42   | Flat2: flat2 → item2 (* non-binding item *)
43 .
44
45 coercion Bind2.
46
47 coercion Flat2.
48
49 (* Basic properties *********************************************************)
50
51 axiom item0_eq_dec: ∀I1,I2:item0. Decidable (I1 = I2).
52
53 (* Basic_1: was: bind_dec *)
54 axiom bind2_eq_dec: ∀I1,I2:bind2. Decidable (I1 = I2).
55
56 (* Basic_1: was: flat_dec *)
57 axiom flat2_eq_dec: ∀I1,I2:flat2. Decidable (I1 = I2).
58
59 (* Basic_1: was: kind_dec *)
60 axiom item2_eq_dec: ∀I1,I2:item2. Decidable (I1 = I2).
61
62 (* Basic_1: removed theorems 21:
63             s_S s_plus s_plus_sym s_minus minus_s_s s_le s_lt s_inj s_inc
64             s_arith0 s_arith1
65             r_S r_plus r_plus_sym r_minus r_dis s_r r_arith0 r_arith1
66             not_abbr_abst bind_dec_not
67 *)