- slicing relation for the global environment defined (gdrop)

[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/substitution/ldrop.ma".
+
+(* GLOBAL ENVIRONMENT SLICING ***********************************************)
+
+inductive gdrop (e:nat) (G1:lenv) : predicate lenv ≝
+| gdrop_lt: ∀G2. e < |G1| → ↓[0, |G1| - (e + 1)] G1 ≡ G2 → gdrop e G1 G2
+| gdrop_ge: |G1| ≤ e → gdrop e G1 (⋆)
+.
+
+interpretation "global slicing" 'RDrop e G1 G2 = (gdrop e G1 G2).
+
+(* basic inversion lemmas ***************************************************)
+
+fact gdrop_inv_atom2_aux: ∀G1,G2,e. ↓[e] G1 ≡ G2 → G2 = ⋆ → |G1| ≤ e.
+#G1 #G2 #e * -G2 //
+#G2 #He #HG12 #H destruct
+lapply (ldrop_fwd_O1_length … HG12) -HG12
+>minus_le_minus_minus_comm // -He >le_plus_minus_comm // <minus_n_n
+>(commutative_plus e) normalize #H destruct
+qed.
+
+lemma gdrop_inv_atom2: ∀G1,e. ↓[e] G1 ≡ ⋆ → |G1| ≤ e.
+/2 width=3/ qed-.
+
+lemma gdrop_inv_ge: ∀G1,G2,e. ↓[e] G1 ≡ G2 → |G1| ≤ e → G2 = ⋆.
+#G1 #G2 #e * // #G2 #H1 #_ #H2
+lapply (lt_to_le_to_lt … H1 H2) -H1 -H2 #He
+elim (lt_refl_false … He)
+qed-.