- degree-based equivalene for terms

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/syntax/append.ma b/matita/matita/contribs/lambdadelta/basic_2/syntax/append.ma
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+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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 "ground_2/notation/functions/append_2.ma".
+include "basic_2/notation/functions/snbind2_3.ma".
+include "basic_2/notation/functions/snabbr_2.ma".
+include "basic_2/notation/functions/snabst_2.ma".
+include "basic_2/syntax/lenv.ma".
+
+(* APPEND FOR LOCAL ENVIRONMENTS ********************************************)
+
+rec definition append L K on K ≝ match K with
+[ LAtom       ⇒ L
+| LPair K I V ⇒ (append L K).ⓑ{I}V
+].
+
+interpretation "append (local environment)" 'Append L1 L2 = (append L1 L2).
+
+interpretation "local environment tail binding construction (binary)"
+   'SnBind2 I T L = (append (LPair LAtom I T) L).
+
+interpretation "tail abbreviation (local environment)"
+   'SnAbbr T L = (append (LPair LAtom Abbr T) L).
+
+interpretation "tail abstraction (local environment)"
+   'SnAbst L T = (append (LPair LAtom Abst T) L).
+
+definition d_appendable_sn: predicate (lenv→relation term) ≝ λR.
+                            ∀K,T1,T2. R K T1 T2 → ∀L. R (L@@K) T1 T2.
+
+(* Basic properties *********************************************************)
+
+lemma append_atom: ∀L. L @@ ⋆ = L.
+// qed.
+
+lemma append_pair: ∀I,L,K,V. L@@(K.ⓑ{I}V) = (L@@K).ⓑ{I}V.
+// qed.
+
+lemma append_atom_sn: ∀L. ⋆@@L = L.
+#L elim L -L //
+#L #I #V >append_pair //
+qed.
+
+lemma append_assoc: associative … append.
+#L1 #L2 #L3 elim L3 -L3 //
+qed.
+
+lemma append_shift: ∀L,K,I,V. L@@(ⓑ{I}V.K) = (L.ⓑ{I}V)@@K.
+#L #K #I #V <append_assoc //
+qed.
+
+(* Basic inversion lemmas ***************************************************)
+
+lemma append_inj_sn: ∀K,L1,L2. L1@@K = L2@@K → L1 = L2.
+#K elim K -K //
+#K #I #V #IH #L1 #L2 >append_pair #H
+elim (destruct_lpair_lpair_aux … H) -H /2 width=1 by/ (**) (* destruct lemma needed *)
+qed-.