+++ /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/relocation/drops_sex.ma".
-
-(* GENERIC SLICING FOR LOCAL ENVIRONMENTS ***********************************)
-
-(* Properties with syntactic equivalence for selected local environments ****)
-
-lemma seq_co_dedropable_sn: co_dedropable_sn seq.
-@sex_liftable_co_dedropable_sn
-/2 width=6 by cfull_lift_sn, ceq_lift_sn/ qed-.
-
-lemma seq_co_dropable_sn: co_dropable_sn seq.
-@sex_co_dropable_sn qed-.
-
-lemma seq_co_dropable_dx: co_dropable_dx seq.
-@sex_co_dropable_dx qed-.
-
-(* Basic_2A1: includes: lreq_drop_trans_be *)
-lemma seq_drops_trans_next: ∀f2,L1,L2. L1 ≡[f2] L2 →
- ∀b,f,I,K2. ⬇*[b, f] L2 ≘ K2.ⓘ{I} → 𝐔⦃f⦄ →
- ∀f1. f ~⊚ ↑f1 ≘ f2 →
- ∃∃K1. ⬇*[b, f] L1 ≘ K1.ⓘ{I} & K1 ≡[f1] K2.
-#f2 #L1 #L2 #HL12 #b #f #I2 #K2 #HLK2 #Hf #f1 #Hf2
-elim (sex_drops_trans_next … HL12 … HLK2 Hf … Hf2) -f2 -L2 -Hf
-#I1 #K1 #HLK1 #HK12 #H <(ceq_ext_inv_eq … H) -I2
-/2 width=3 by ex2_intro/
-qed-.
-
-(* Basic_2A1: includes: lreq_drop_conf_be *)
-lemma seq_drops_conf_next: ∀f2,L1,L2. L1 ≡[f2] L2 →
- ∀b,f,I,K1. ⬇*[b, f] L1 ≘ K1.ⓘ{I} → 𝐔⦃f⦄ →
- ∀f1. f ~⊚ ↑f1 ≘ f2 →
- ∃∃K2. ⬇*[b, f] L2 ≘ K2.ⓘ{I} & K1 ≡[f1] K2.
-#f2 #L1 #L2 #HL12 #b #f #I1 #K1 #HLK1 #Hf #f1 #Hf2
-elim (seq_drops_trans_next … (seq_sym … HL12) … HLK1 … Hf2) // -f2 -L1 -Hf
-/3 width=3 by seq_sym, ex2_intro/
-qed-.
-
-lemma drops_seq_trans_next: ∀f1,K1,K2. K1 ≡[f1] K2 →
- ∀b,f,I,L1. ⬇*[b, f] L1.ⓘ{I} ≘ K1 →
- ∀f2. f ~⊚ f1 ≘ ↑f2 →
- ∃∃L2. ⬇*[b, f] L2.ⓘ{I} ≘ K2 & L1 ≡[f2] L2 & L1.ⓘ{I} ≡[f] L2.ⓘ{I}.
-#f1 #K1 #K2 #HK12 #b #f #I1 #L1 #HLK1 #f2 #Hf2
-elim (drops_sex_trans_next … HK12 … HLK1 … Hf2) -f1 -K1
-/2 width=6 by cfull_lift_sn, ceq_lift_sn/
-#I2 #L2 #HLK2 #HL12 #H >(ceq_ext_inv_eq … H) -I1
-/2 width=4 by ex3_intro/
-qed-.