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14
15 (* THE FORMAL SYSTEM λδ - MATITA SOURCE SCRIPTS 
16  * Specification started: 2011 April 17
17  * - Patience on me so that I gain peace and perfection! -
18  * [ suggested invocation to start formal specifications with ]
19  *)
20
21 include "Ground-2/list.ma".
22 include "Basic-2/notation.ma".
23
24 (* ITEMS ********************************************************************)
25
26 (* atomic items *)
27 inductive item0: Type[0] ≝
28    | Sort: nat → item0 (* sort: starting at 0 *)
29    | LRef: nat → item0 (* reference by index: starting at 0 *)
30 .
31
32 (* binary binding items *)
33 inductive bind2: Type[0] ≝
34   | Abbr: bind2 (* abbreviation *)
35   | Abst: bind2 (* abstraction *)
36 .
37
38 (* binary non-binding items *)
39 inductive flat2: Type[0] ≝
40   | Appl: flat2 (* application *)
41   | Cast: flat2 (* explicit type annotation *)
42 .
43
44 (* binary items *)
45 inductive item2: Type[0] ≝
46   | Bind: bind2 → item2 (* binding item *)
47   | Flat: flat2 → item2 (* non-binding item *)
48 .
49
50 coercion item2_of_bind2: ∀I:bind2.item2 ≝ Bind on _I:bind2 to item2.
51
52 coercion item2_of_flat2: ∀I:flat2.item2 ≝ Flat on _I:flat2 to item2.
53
54 (* Basic-1: removed theorems 19:
55             s_S s_plus s_plus_sym s_minus minus_s_s s_le s_lt s_inj s_inc
56             s_arith0 s_arith1
57             r_S r_plus r_plus_sym r_minus r_dis s_r r_arith0 r_arith1
58 *)