syntactic components detached from basic_2 become static_2

[helm.git] / matita / matita / contribs / lambdadelta / static_2 / syntax / genv.ma

diff --git a/matita/matita/contribs/lambdadelta/static_2/syntax/genv.ma b/matita/matita/contribs/lambdadelta/static_2/syntax/genv.ma
new file mode 100644 (file)
index 0000000..35365d8
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/static_2/syntax/genv.ma
@@ -0,0 +1,52 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+include "static_2/notation/functions/star_0.ma".
+include "static_2/notation/functions/dxbind2_3.ma".
+include "static_2/notation/functions/dxabbr_2.ma".
+include "static_2/notation/functions/dxabst_2.ma".
+include "static_2/syntax/term.ma".
+
+(* GLOBAL ENVIRONMENTS ******************************************************)
+
+(* global environments *)
+inductive genv: Type[0] ≝
+| GAtom: genv                       (* empty *)
+| GPair: genv → bind2 → term → genv (* binary binding construction *)
+.
+
+interpretation "sort (global environment)"
+   'Star = (GAtom).
+
+interpretation "global environment binding construction (binary)"
+   'DxBind2 G I T = (GPair G I T).
+
+interpretation "abbreviation (global environment)"
+   'DxAbbr G T = (GPair G Abbr T).
+
+interpretation "abstraction (global environment)"
+   'DxAbst G T = (GPair G Abst T).
+
+(* Basic properties *********************************************************)
+
+lemma eq_genv_dec: ∀G1,G2:genv. Decidable (G1 = G2).
+#G1 elim G1 -G1 [| #G1 #I1 #T1 #IHG1 ] * [2,4: #G2 #I2 #T2 ]
+[3: /2 width=1 by or_introl/
+|2: elim (eq_bind2_dec I1 I2) #HI
+    [ elim (IHG1 G2) -IHG1 #HG 
+      [ elim (eq_term_dec T1 T2) #HT /2 width=1 by or_introl/ ]
+    ]
+]
+@or_intror #H destruct /2 width=1 by/
+qed-.