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[helm.git] / matita / matita / contribs / lambda_delta / Basic_2 / substitution / gdrop.ma

diff --git a/matita/matita/contribs/lambda_delta/Basic_2/substitution/gdrop.ma b/matita/matita/contribs/lambda_delta/Basic_2/substitution/gdrop.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 "Basic_2/grammar/genv.ma".
-
-(* GLOBAL ENVIRONMENT SLICING ***********************************************)
-
-inductive gdrop (e:nat): relation genv ≝
-| gdrop_gt: ∀G. |G| ≤ e → gdrop e G (⋆)
-| gdrop_eq: ∀G. |G| = e + 1 → gdrop e G G
-| gdrop_lt: ∀I,G1,G2,V. e < |G1| → gdrop e G1 G2 → gdrop e (G1. ⓑ{I} V) G2
-.
-
-interpretation "global slicing" 
-   'RDrop e G1 G2 = (gdrop e G1 G2).
-
-(* basic inversion lemmas ***************************************************)
-
-lemma gdrop_inv_gt: ∀G1,G2,e. ⇩[e] G1 ≡ G2 → |G1| ≤ e → G2 = ⋆.
-#G1 #G2 #e * -G1 -G2 //
-[ #G #H >H -H >commutative_plus #H
-  lapply (le_plus_to_le_r … 0 H) -H #H
-  lapply (le_n_O_to_eq … H) -H #H destruct
-| #I #G1 #G2 #V #H1 #_ #H2
-  lapply (le_to_lt_to_lt … H2 H1) -H2 -H1 normalize in ⊢ (? % ? → ?); >commutative_plus #H
-  lapply (lt_plus_to_lt_l … 0 H) -H #H
-  elim (lt_zero_false … H)
-]
-qed-.
-
-lemma gdrop_inv_eq: ∀G1,G2,e. ⇩[e] G1 ≡ G2 → |G1| = e + 1 → G1 = G2.
-#G1 #G2 #e * -G1 -G2 //
-[ #G #H1 #H2 >H2 in H1; -H2 >commutative_plus #H
-  lapply (le_plus_to_le_r … 0 H) -H #H
-  lapply (le_n_O_to_eq … H) -H #H destruct
-| #I #G1 #G2 #V #H1 #_ normalize #H2
-  <(injective_plus_l … H2) in H1; -H2 #H
-  elim (lt_refl_false … H)
-]
-qed-.
-
-fact gdrop_inv_lt_aux: ∀I,G,G1,G2,V,e. ⇩[e] G ≡ G2 → G = G1. ⓑ{I} V →
-                       e < |G1| → ⇩[e] G1 ≡ G2.
-#I #G #G1 #G2 #V #e * -G -G2
-[ #G #H1 #H destruct #H2
-  lapply (le_to_lt_to_lt … H1 H2) -H1 -H2 normalize in ⊢ (? % ? → ?); >commutative_plus #H
-  lapply (lt_plus_to_lt_l … 0 H) -H #H
-  elim (lt_zero_false … H)
-| #G #H1 #H2 destruct >(injective_plus_l … H1) -H1 #H
-  elim (lt_refl_false … H)
-| #J #G #G2 #W #_ #HG2 #H destruct //
-]
-qed.
-
-lemma gdrop_inv_lt: ∀I,G1,G2,V,e.
-                    ⇩[e] G1. ⓑ{I} V ≡ G2 → e < |G1| → ⇩[e] G1 ≡ G2.
-/2 width=5/ qed-.
-
-(* Basic properties *********************************************************)
-
-lemma gdrop_total: ∀e,G1. ∃G2. ⇩[e] G1 ≡ G2.
-#e #G1 elim G1 -G1 /3 width=2/
-#I #V #G1 * #G2 #HG12
-elim (lt_or_eq_or_gt e (|G1|)) #He
-[ /3 width=2/
-| destruct /3 width=2/
-| @ex_intro [2: @gdrop_gt normalize /2 width=1/ | skip ] (**) (* explicit constructor *)
-]
-qed.