syntactic components detached from basic_2 become static_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / syntax / aarity.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/syntax/aarity.ma b/matita/matita/contribs/lambdadelta/basic_2/syntax/aarity.ma
deleted file mode 100644 (file)
index 4db5d31..0000000
--- a/matita/matita/contribs/lambdadelta/basic_2/syntax/aarity.ma
+++ /dev/null
@@ -1,74 +0,0 @@
-(**************************************************************************)
-(*       ___                                                              *)
-(*      ||M||                                                             *)
-(*      ||A||       A project by Andrea Asperti                           *)
-(*      ||T||                                                             *)
-(*      ||I||       Developers:                                           *)
-(*      ||T||         The HELM team.                                      *)
-(*      ||A||         http://helm.cs.unibo.it                             *)
-(*      \   /                                                             *)
-(*       \ /        This file is distributed under the terms of the       *)
-(*        v         GNU General Public License Version 2                  *)
-(*                                                                        *)
-(**************************************************************************)
-
-(* THE FORMAL SYSTEM λδ: MATITA SOURCE FILES
- * Initial invocation: - Patience on me to gain peace and perfection! -
- *)
-
-include "ground_2/lib/relations.ma".
-include "basic_2/notation/constructors/item0_0.ma".
-include "basic_2/notation/constructors/snitem2_2.ma".
-
-(* ATOMIC ARITY *************************************************************)
-
-inductive aarity: Type[0] ≝
-  | AAtom: aarity                   (* atomic aarity construction *)
-  | APair: aarity → aarity → aarity (* binary aarity construction *)
-.
-
-interpretation "atomic arity construction (atomic)"
-   'Item0 = AAtom.
-
-interpretation "atomic arity construction (binary)"
-   'SnItem2 A1 A2 = (APair A1 A2).
-
-(* Basic inversion lemmas ***************************************************)
-
-fact destruct_apair_apair_aux: ∀A1,A2,B1,B2. ②B1.A1 = ②B2.A2 → B1 = B2 ∧ A1 = A2.
-#A1 #A2 #B1 #B2 #H destruct /2 width=1 by conj/
-qed-.
-
-lemma discr_apair_xy_x: ∀A,B. ②B.A = B → ⊥.
-#A #B elim B -B
-[ #H destruct
-| #Y #X #IHY #_ #H elim (destruct_apair_apair_aux … H) -H /2 width=1 by/ (**) (* destruct lemma needed *)
-]
-qed-.
-
-(* Basic_2A1: was: discr_tpair_xy_y *)
-lemma discr_apair_xy_y: ∀B,A. ②B. A = A → ⊥.
-#B #A elim A -A
-[ #H destruct
-| #Y #X #_ #IHX #H elim (destruct_apair_apair_aux … H) -H /2 width=1 by/ (**) (* destruct lemma needed *)
-]
-qed-.
-
-(* Basic properties *********************************************************)
-
-lemma eq_aarity_dec: ∀A1,A2:aarity. Decidable (A1 = A2).
-#A1 elim A1 -A1
-[ #A2 elim A2 -A2 /2 width=1 by or_introl/
-  #B2 #A2 #_ #_ @or_intror #H destruct
-| #B1 #A1 #IHB1 #IHA1 #A2 elim A2 -A2
-  [ -IHB1 -IHA1 @or_intror #H destruct
-  | #B2 #A2 #_ #_ elim (IHB1 B2) -IHB1
-    [ #H destruct elim (IHA1 A2) -IHA1
-      [ #H destruct /2 width=1 by or_introl/
-      | #HA12 @or_intror #H destruct /2 width=1 by/
-      ]
-    | -IHA1 #HB12 @or_intror #H destruct /2 width=1 by/
-    ]
-  ]
-]
-qed-.