theory of generic slicing almost completed ....

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / relocation / drops_weight.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/relocation/drops_weight.ma b/matita/matita/contribs/lambdadelta/basic_2/relocation/drops_weight.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/cl_restricted_weight.ma".
+include "basic_2/relocation/lifts_weight.ma".
+include "basic_2/relocation/drops.ma".
+
+(* GENERAL SLICING FOR LOCAL ENVIRONMENTS ***********************************)
+
+(* Forward lemmas on weight for local environments **************************)
+
+(* Basic_2A1: includes: drop_fwd_lw *)
+lemma drops_fwd_lw: ∀L1,L2,s,t. ⬇*[s, t] L1 ≡ L2 → ♯{L2} ≤ ♯{L1}.
+#L1 #L2 #s #t #H elim H -L1 -L2 -t //
+[ /2 width=3 by transitive_le/
+| #I #L1 #L2 #V1 #V2 #t #_ #HV21 #IHL12 normalize
+  >(lifts_fwd_tw … HV21) -HV21 /2 width=1 by monotonic_le_plus_l/
+]
+qed-.
+
+(* Basic_2A1: includes: drop_fwd_lw_lt *)
+(* Note: 𝐈⦃t⦄ → ⊥ is ∥l∥ < |L| *)
+lemma drops_fwd_lw_lt: ∀L1,L2,t. ⬇*[Ⓕ, t] L1 ≡ L2 →
+                       (𝐈⦃t⦄ → ⊥) → ♯{L2} < ♯{L1}.
+#L1 #L2 #t #H elim H -L1 -L2 -t
+[ #t #Ht #Hnt elim Hnt -Hnt /2 width=1 by/
+| /3 width=3 by drops_fwd_lw, le_to_lt_to_lt/
+| #I #L1 #L2 #V1 #V2 #t #_ #HV21 #IHL12 #H normalize in ⊢ (?%%); -I
+  >(lifts_fwd_tw … HV21) -V2 /4 width=1 by monotonic_lt_plus_l/
+]
+qed-.
+
+(* Forward lemmas on restricted weight for closures *************************)
+
+(* Basic_2A1: includes: drop_fwd_rfw *)
+lemma drops_pair2_fwd_rfw: ∀I,L,K,V,s,t. ⬇*[s, t] L ≡ K.ⓑ{I}V → ∀T. ♯{K, V} < ♯{L, T}.
+#I #L #K #V #s #t #HLK lapply (drops_fwd_lw … HLK) -HLK
+normalize in ⊢ (%→?→?%%); /3 width=3 by le_to_lt_to_lt/
+qed-.