X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fsyntax%2Faarity.ma;fp=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fsyntax%2Faarity.ma;h=7f44246c7bde31c709c73a12f6e770df1d76c5a6;hb=09b4420070d6a71990e16211e499b51dbb0742cb;hp=0000000000000000000000000000000000000000;hpb=bba53a83579540bc3925d47d679e2aad22e85755;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/basic_2/syntax/aarity.ma b/matita/matita/contribs/lambdadelta/basic_2/syntax/aarity.ma
new file mode 100644
index 000000000..7f44246c7
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/basic_2/syntax/aarity.ma
@@ -0,0 +1,73 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/star.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-.
+
+lemma discr_tpair_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-.