syntactic components detached from basic_2 become static_2

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

diff --git a/matita/matita/contribs/lambdadelta/static_2/syntax/lenv.ma b/matita/matita/contribs/lambdadelta/static_2/syntax/lenv.ma
new file mode 100644 (file)
index 0000000..7e2b65d
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/static_2/syntax/lenv.ma
@@ -0,0 +1,89 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/dxitem_2.ma".
+include "static_2/notation/functions/dxbind1_2.ma".
+include "static_2/notation/functions/dxbind2_3.ma".
+include "static_2/notation/functions/dxvoid_1.ma".
+include "static_2/notation/functions/dxabbr_2.ma".
+include "static_2/notation/functions/dxabst_2.ma".
+include "static_2/syntax/bind.ma".
+
+(* LOCAL ENVIRONMENTS *******************************************************)
+
+(* local environments *)
+inductive lenv: Type[0] ≝
+| LAtom: lenv               (* empty *)
+| LBind: lenv → bind → lenv (* binding construction *)
+.
+
+interpretation "sort (local environment)"
+   'Star = LAtom.
+
+interpretation "local environment binding construction (generic)"
+   'DxItem L I = (LBind L I).
+
+interpretation "local environment binding construction (unary)"
+   'DxBind1 L I = (LBind L (BUnit I)).
+
+interpretation "local environment binding construction (binary)"
+   'DxBind2 L I T = (LBind L (BPair I T)).
+
+interpretation "void (local environment)"
+   'DxVoid L = (LBind L (BUnit Void)).
+
+interpretation "abbreviation (local environment)"
+   'DxAbbr L T = (LBind L (BPair Abbr T)).
+
+interpretation "abstraction (local environment)"
+   'DxAbst L T = (LBind L (BPair Abst T)).
+
+definition cfull: relation3 lenv bind bind ≝ λL,I1,I2. ⊤.
+
+definition ceq: relation3 lenv term term ≝ λL. eq ….
+
+(* Basic properties *********************************************************)
+
+lemma eq_lenv_dec: ∀L1,L2:lenv. Decidable (L1 = L2).
+#L1 elim L1 -L1 [| #L1 #I1 #IHL1 ] * [2,4: #L2 #I2 ]
+[3: /2 width=1 by or_introl/
+|2: elim (eq_bind_dec I1 I2) #HI
+    [ elim (IHL1 L2) -IHL1 #HL /2 width=1 by or_introl/ ]
+]
+@or_intror #H destruct /2 width=1 by/
+qed-.
+
+lemma cfull_dec: ∀L,T1,T2. Decidable (cfull L T1 T2).
+/2 width=1 by or_introl/ qed-.
+
+(* Basic inversion lemmas ***************************************************)
+
+fact destruct_lbind_lbind_aux: ∀I1,I2,L1,L2. L1.ⓘ{I1} = L2.ⓘ{I2} →
+                               L1 = L2 ∧ I1 = I2.
+#I1 #I2 #L1 #L2 #H destruct /2 width=1 by conj/
+qed-.
+
+(* Basic_2A1: uses: discr_lpair_x_xy *)
+lemma discr_lbind_x_xy: ∀I,L. L = L.ⓘ{I} → ⊥.
+#I #L elim L -L
+[ #H destruct
+| #L #J #IHL #H elim (destruct_lbind_lbind_aux … H) -H  (**) (* destruct lemma needed *)
+  #H1 #H2 destruct /2 width=1 by/
+]
+qed-.
+
+(* Basic_2A1: uses: discr_lpair_xy_x *)
+lemma discr_lbind_xy_x: ∀I,L. L.ⓘ{I} = L → ⊥.
+/2 width=4 by discr_lbind_x_xy/ qed-.