update in ground_2 and basic_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/syntax/genv.ma b/matita/matita/contribs/lambdadelta/basic_2/syntax/genv.ma
index 8483917c478dbc58e17735b6461727f65ec0b7fe..085e35dac7d0e8b484c8f5a9bf0cc79ea792d973 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/syntax/genv.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/syntax/genv.ma
@@ -12,7 +12,6 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "ground_2/lib/list2.ma".
 include "basic_2/notation/constructors/star_0.ma".
 include "basic_2/notation/constructors/dxbind2_3.ma".
 include "basic_2/notation/constructors/dxabbr_2.ma".
@@ -22,20 +21,32 @@ include "basic_2/syntax/term.ma".
 (* GLOBAL ENVIRONMENTS ******************************************************)
 
 (* global environments *)
-definition genv ≝ list2 bind2 term.
+inductive genv: Type[0] ≝
+| GAtom: genv                       (* empty *)
+| GBind: genv → bind2 → term → genv (* binding construction *)
+.
 
 interpretation "sort (global environment)"
-   'Star = (nil2 bind2 term).
+   'Star = (GAtom).
 
 interpretation "global environment binding construction (binary)"
-   'DxBind2 L I T = (cons2 bind2 term I T L).
+   'DxBind2 G I T = (GBind G I T).
 
 interpretation "abbreviation (global environment)"
-   'DxAbbr L T = (cons2 bind2 term Abbr T L).
+   'DxAbbr G T = (GBind G Abbr T).
 
 interpretation "abstraction (global environment)"
-   'DxAbst L T = (cons2 bind2 term Abst T L).
+   'DxAbst G T = (GBind G Abst T).
 
 (* Basic properties *********************************************************)
 
-axiom eq_genv_dec: ∀G1,G2:genv. Decidable (G1 = G2).
+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-.