- new component "s_transition" for the restored fqu and fquq

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / grammar / lenv_append.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/grammar/lenv_append.ma b/matita/matita/contribs/lambdadelta/basic_2/grammar/lenv_append.ma
deleted file mode 100644 (file)
index aa2e587..0000000
--- a/matita/matita/contribs/lambdadelta/basic_2/grammar/lenv_append.ma
+++ /dev/null
@@ -1,141 +0,0 @@
-(**************************************************************************)
-(*       ___                                                              *)
-(*      ||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/grammar/lenv_length.ma".
-
-(* LOCAL ENVIRONMENTS *******************************************************)
-
-let rec 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_length: ∀L1,L2. |L1 @@ L2| = |L1| + |L2|.
-#L1 #L2 elim L2 -L2 //
-#L2 #I #V2 >append_pair >length_pair >length_pair //
-qed.
-
-lemma ltail_length: ∀I,L,V. |ⓑ{I}V.L| = ⫯|L|.
-#I #L #V >append_length //
-qed.
-
-(* Basic_1: was just: chead_ctail *)
-lemma lpair_ltail: ∀L,I,V. ∃∃J,K,W. L.ⓑ{I}V = ⓑ{J}W.K & |L| = |K|.
-#L elim L -L /2 width=5 by ex2_3_intro/
-#L #Z #X #IHL #I #V elim (IHL Z X) -IHL
-#J #K #W #H #_ >H -H >ltail_length
-@(ex2_3_intro … J (K.ⓑ{I}V) W) /2 width=1 by length_pair/
-qed-.
-
-(* Basic inversion lemmas ***************************************************)
-
-lemma append_inj_sn: ∀K1,K2,L1,L2. L1 @@ K1 = L2 @@ K2 → |K1| = |K2| →
-                     L1 = L2 ∧ K1 = K2.
-#K1 elim K1 -K1
-[ * /2 width=1 by conj/
-  #K2 #I2 #V2 #L1 #L2 #_ >length_atom >length_pair
-  #H destruct
-| #K1 #I1 #V1 #IH *
-  [ #L1 #L2 #_ >length_atom >length_pair
-    #H destruct
-  | #K2 #I2 #V2 #L1 #L2 #H1 #H2
-    elim (destruct_lpair_lpair_aux … H1) -H1 #H1 #H3 #H4 destruct (**) (* destruct lemma needed *)
-    elim (IH … H1) -IH -H1 /2 width=1 by conj/
-  ]
-]
-qed-.
-
-(* Note: lemma 750 *)
-lemma append_inj_dx: ∀K1,K2,L1,L2. L1 @@ K1 = L2 @@ K2 → |L1| = |L2| →
-                     L1 = L2 ∧ K1 = K2.
-#K1 elim K1 -K1
-[ * /2 width=1 by conj/
-  #K2 #I2 #V2 #L1 #L2 >append_atom >append_pair #H destruct
-  >length_pair >append_length >plus_n_Sm
-  #H elim (plus_xSy_x_false … H)
-| #K1 #I1 #V1 #IH *
-  [ #L1 #L2 >append_pair >append_atom #H destruct
-    >length_pair >append_length >plus_n_Sm #H
-    lapply (discr_plus_x_xy … H) -H #H destruct
-  | #K2 #I2 #V2 #L1 #L2 >append_pair >append_pair #H1 #H2
-    elim (destruct_lpair_lpair_aux … H1) -H1 #H1 #H3 #H4 destruct (**) (* destruct lemma needed *)
-    elim (IH … H1) -IH -H1 /2 width=1 by conj/
-  ]
-]
-qed-.
-
-lemma append_inv_refl_dx: ∀L,K. L @@ K = L → K = ⋆.
-#L #K #H elim (append_inj_dx … (⋆) … H) //
-qed-.
-
-lemma append_inv_pair_dx: ∀I,L,K,V. L @@ K = L.ⓑ{I}V → K = ⋆.ⓑ{I}V.
-#I #L #K #V #H elim (append_inj_dx … (⋆.ⓑ{I}V) … H) //
-qed-.
-
-lemma length_inv_pos_dx_ltail: ∀L,l. |L| = ⫯l →
-                               ∃∃I,K,V. |K| = l & L = ⓑ{I}V.K.
-#Y #l #H elim (length_inv_succ_dx … H) -H #I #L #V #Hl #HLK destruct
-elim (lpair_ltail L I V) /2 width=5 by ex2_3_intro/
-qed-.
-
-lemma length_inv_pos_sn_ltail: ∀L,l. ⫯l = |L| →
-                               ∃∃I,K,V. l = |K| & L = ⓑ{I}V.K.
-#Y #l #H elim (length_inv_succ_sn … H) -H #I #L #V #Hl #HLK destruct
-elim (lpair_ltail L I V) /2 width=5 by ex2_3_intro/
-qed-.
-
-(* Basic eliminators ********************************************************)
-
-(* Basic_1: was: c_tail_ind *)
-lemma lenv_ind_alt: ∀R:predicate lenv.
-                    R (⋆) → (∀I,L,T. R L → R (ⓑ{I}T.L)) →
-                    ∀L. R L.
-#R #IH1 #IH2 #L @(f_ind … length … L) -L #x #IHx * // -IH1
-#L #I #V #H destruct elim (lpair_ltail L I V) /4 width=1 by/
-qed-.