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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 *)
10 (* \ / This file is distributed under the terms of the *)
11 (* v GNU General Public License Version 2 *)
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15 (* THE FORMAL SYSTEM λδ - MATITA SOURCE FILES
16 * Confluence of context-sensitive parallel reduction closed: 2011 September 21
17 * Confluence of context-free parallel reduction closed: 2011 September 6
18 * Specification started: 2011 April 17
19 * - Patience on me to gain peace and perfection! -
20 * [ suggested invocation to start formal specifications with ]
23 include "Ground_2/star.ma".
24 include "Basic_2/notation.ma".
26 (* ATOMIC ARITY *************************************************************)
28 inductive aarity: Type[0] ≝
29 | AAtom: aarity (* atomic aarity construction *)
30 | APair: aarity → aarity → aarity (* binary aarity construction *)
33 interpretation "aarity construction (atomic)"
36 interpretation "aarity construction (binary)"
37 'SnItem2 A1 A2 = (APair A1 A2).
39 (* Basic inversion lemmas ***************************************************)
41 lemma discr_apair_xy_x: ∀A,B. ②B. A = B → False.
44 | #Y #X #IHY #_ #H destruct
45 -H >e0 in e1; normalize (**) (* destruct: one quality is not simplified, the destucted equality is not erased *)
50 lemma discr_tpair_xy_y: ∀B,A. ②B. A = A → False.
53 | #Y #X #_ #IHX #H destruct
54 -H (**) (* destruct: the destucted equality is not erased *)
59 (* Basic properties *********************************************************)
61 lemma aarity_eq_dec: ∀A1,A2:aarity. Decidable (A1 = A2).
63 [ #A2 elim A2 -A2 /2 width=1/
64 #B2 #A2 #_ #_ @or_intror #H destruct
65 | #B1 #A1 #IHB1 #IHA1 #A2 elim A2 -A2
66 [ -IHB1 -IHA1 @or_intror #H destruct
67 | #B2 #A2 #_ #_ elim (IHB1 B2) -IHB1
68 [ #H destruct elim (IHA1 A2) -IHA1
69 [ #H destruct /2 width=1/
70 | #HA12 @or_intror #H destruct /2 width=1/
72 | -IHA1 #HB12 @or_intror #H destruct /2 width=1/