+++ /dev/null
-(**************************************************************************)
-(* ___ *)
-(* ||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/syntax/cl_restricted_weight.ma".
-include "basic_2/relocation/lifts_weight_bind.ma".
-include "basic_2/relocation/drops.ma".
-
-(* GENERIC SLICING FOR LOCAL ENVIRONMENTS ***********************************)
-
-(* Forward lemmas with weight for local environments ************************)
-
-(* Basic_2A1: includes: drop_fwd_lw *)
-lemma drops_fwd_lw: ∀b,f,L1,L2. ⬇*[b, f] L1 ≘ L2 → ♯{L2} ≤ ♯{L1}.
-#b #f #L1 #L2 #H elim H -f -L1 -L2 //
-[ /2 width=3 by transitive_le/
-| #f #I1 #I2 #L1 #L2 #_ #HI21 #IHL12 normalize
- >(liftsb_fwd_bw … HI21) -HI21 /2 width=1 by monotonic_le_plus_l/
-]
-qed-.
-
-(* Basic_2A1: includes: drop_fwd_lw_lt *)
-lemma drops_fwd_lw_lt: ∀f,L1,L2. ⬇*[Ⓣ, f] L1 ≘ L2 →
- (𝐈⦃f⦄ → ⊥) → ♯{L2} < ♯{L1}.
-#f #L1 #L2 #H elim H -f -L1 -L2
-[ #f #Hf #Hnf elim Hnf -Hnf /2 width=1 by/
-| /3 width=3 by drops_fwd_lw, le_to_lt_to_lt/
-| #f #I1 #I2 #L1 #L2 #_ #HI21 #IHL12 #H normalize in ⊢ (?%%);
- >(liftsb_fwd_bw … HI21) -I2 /5 width=3 by isid_push, monotonic_lt_plus_l/
-]
-qed-.
-
-(* Forward lemmas with restricted weight for closures ***********************)
-
-(* Basic_2A1: includes: drop_fwd_rfw *)
-lemma drops_bind2_fwd_rfw: ∀b,f,I,L,K,V. ⬇*[b, f] L ≘ K.ⓑ{I}V → ∀T. ♯{K, V} < ♯{L, T}.
-#b #f #I #L #K #V #HLK lapply (drops_fwd_lw … HLK) -HLK
-normalize in ⊢ (%→?→?%%); /3 width=3 by le_to_lt_to_lt, monotonic_lt_plus_r/
-qed-.
-
-(* Advanced inversion lemma *************************************************)
-
-lemma drops_inv_x_bind_xy: ∀b,f,I,L. ⬇*[b, f] L ≘ L.ⓘ{I} → ⊥.
-#b #f #I #L #H lapply (drops_fwd_lw … H) -b -f
-/2 width=4 by lt_le_false/ (**) (* full auto is a bit slow: 19s *)
-qed-.