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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 *)
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15 (* THE FORMAL SYSTEM λδ: MATITA SOURCE FILES
16 * Initial invocation: - Patience on me to gain peace and perfection! -
19 include "ground_2/star.ma".
20 include "basic_2/notation.ma".
22 (* ATOMIC ARITY *************************************************************)
24 inductive aarity: Type[0] ≝
25 | AAtom: aarity (* atomic aarity construction *)
26 | APair: aarity → aarity → aarity (* binary aarity construction *)
29 interpretation "aarity construction (atomic)"
32 interpretation "aarity construction (binary)"
33 'SnItem2 A1 A2 = (APair A1 A2).
35 (* Basic inversion lemmas ***************************************************)
37 lemma discr_apair_xy_x: ∀A,B. ②B. A = B → ⊥.
40 | #Y #X #IHY #_ #H destruct
41 -H >e0 in e1; normalize (**) (* destruct: one quality is not simplified, the destucted equality is not erased *)
46 lemma discr_tpair_xy_y: ∀B,A. ②B. A = A → ⊥.
49 | #Y #X #_ #IHX #H destruct
50 -H (**) (* destruct: the destucted equality is not erased *)
55 (* Basic properties *********************************************************)
57 lemma aarity_eq_dec: ∀A1,A2:aarity. Decidable (A1 = A2).
59 [ #A2 elim A2 -A2 /2 width=1/
60 #B2 #A2 #_ #_ @or_intror #H destruct
61 | #B1 #A1 #IHB1 #IHA1 #A2 elim A2 -A2
62 [ -IHB1 -IHA1 @or_intror #H destruct
63 | #B2 #A2 #_ #_ elim (IHB1 B2) -IHB1
64 [ #H destruct elim (IHA1 A2) -IHA1
65 [ #H destruct /2 width=1/
66 | #HA12 @or_intror #H destruct /2 width=1/
68 | -IHA1 #HB12 @or_intror #H destruct /2 width=1/