- lambda_delta: programmed renaming to lambdadelta

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

diff --git a/matita/matita/contribs/lambda_delta/basic_2/grammar/lenv_append.ma b/matita/matita/contribs/lambda_delta/basic_2/grammar/lenv_append.ma
deleted file mode 100644 (file)
index ab90ddf..0000000
--- a/matita/matita/contribs/lambda_delta/basic_2/grammar/lenv_append.ma
+++ /dev/null
@@ -1,130 +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 "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).
-
-(* Basic properties *********************************************************)
-
-lemma append_atom_sn: ∀L. ⋆ @@ L = L.
-#L elim L -L normalize //
-qed.
-
-lemma append_assoc: associative … append.
-#L1 #L2 #L3 elim L3 -L3 normalize //
-qed.
-
-lemma append_length: ∀L1,L2. |L1 @@ L2| = |L1| + |L2|.
-#L1 #L2 elim L2 -L2 normalize //
-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
-[ * normalize /2 width=1/
-  #K2 #I2 #V2 #L1 #L2 #_ <plus_n_Sm #H destruct
-| #K1 #I1 #V1 #IH * normalize
-  [ #L1 #L2 #_ <plus_n_Sm #H destruct
-  | #K2 #I2 #V2 #L1 #L2 #H1 #H2
-    elim (destruct_lpair_lpair … H1) -H1 #H1 #H3 #H4 destruct (**) (* destruct lemma needed *)
-    elim (IH … H1 ?) -IH -H1 // -H2 /2 width=1/
-  ]
-]
-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
-[ * normalize /2 width=1/
-  #K2 #I2 #V2 #L1 #L2 #H1 #H2 destruct
-  normalize in H2; >append_length in H2; #H
-  elim (plus_xySz_x_false … H)
-| #K1 #I1 #V1 #IH * normalize
-  [ #L1 #L2 #H1 #H2 destruct
-    normalize in H2; >append_length in H2; #H
-    elim (plus_xySz_x_false … (sym_eq … H))
-  | #K2 #I2 #V2 #L1 #L2 #H1 #H2
-    elim (destruct_lpair_lpair … H1) -H1 #H1 #H3 #H4 destruct (**) (* destruct lemma needed *)
-    elim (IH … H1 ?) -IH -H1 // -H2 /2 width=1/
-  ]
-]
-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_append: ∀d,L. |L| = d + 1 →
-                                ∃∃I,K,V. |K| = d & L = ⋆.ⓑ{I}V @@ K.
-#d @(nat_ind_plus … d) -d
-[ #L #H 
-  elim (length_inv_pos_dx … H) -H #I #K #V #H
-  >(length_inv_zero_dx … H) -H #H destruct
-  @ex2_3_intro [4: /2 width=2/ |5: // |1,2,3: skip ] (**) (* /3/ does not work *)
-| #d #IHd #L #H
-  elim (length_inv_pos_dx … H) -H #I #K #V #H
-  elim (IHd … H) -IHd -H #I0 #K0 #V0 #H1 #H2 #H3 destruct
-  @(ex2_3_intro … (K0.ⓑ{I}V)) //
-]
-qed-.
-
-(* Basic_eliminators ********************************************************)
-
-fact lenv_ind_dx_aux: ∀R:predicate lenv. R ⋆ →
-                      (∀I,L,V. R L → R (⋆.ⓑ{I}V @@ L)) →
-                      ∀d,L. |L| = d → R L.
-#R #Hatom #Hpair #d @(nat_ind_plus … d) -d
-[ #L #H >(length_inv_zero_dx … H) -H //
-| #d #IH #L #H
-  elim (length_inv_pos_dx_append … H) -H #I #K #V #H1 #H2 destruct /3 width=1/
-]
-qed-.
-
-lemma lenv_ind_dx: ∀R:predicate lenv. R ⋆ →
-                   (∀I,L,V. R L → R (⋆.ⓑ{I}V @@ L)) →
-                   ∀L. R L.
-/3 width=2 by lenv_ind_dx_aux/ qed-.
-
-(* Advanced inversion lemmas ************************************************)
-
-lemma length_inv_pos_sn_append: ∀d,L. 1 + d = |L| →
-                                ∃∃I,K,V. d = |K| & L = ⋆. ⓑ{I}V @@ K.
-#d >commutative_plus @(nat_ind_plus … d) -d
-[ #L #H elim (length_inv_pos_sn … H) -H #I #K #V #H1 #H2 destruct
-  >(length_inv_zero_sn … H1) -K
-  @(ex2_3_intro … (⋆)) // (**) (* explicit constructor *)
-| #d #IHd #L #H elim (length_inv_pos_sn … H) -H #I #K #V #H1 #H2 destruct
-  >H1 in IHd; -H1 #IHd
-  elim (IHd K ?) -IHd // #J #L #W #H1 #H2 destruct
-  @(ex2_3_intro … (L.ⓑ{I}V)) // (**) (* explicit constructor *)
-  >append_length /2 width=1/
-]
-qed-.