+++ /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.ma".
-include "basic_2/static/lsuba.ma".
-
-(* RESTRICTED REFINEMENT FOR ATOMIC ARITY ASSIGNMENT ************************)
-
-(* Properties with generic slicing for local environments *******************)
-
-(* Note: the premise 𝐔⦃f⦄ cannot be removed *)
-(* Basic_2A1: includes: lsuba_drop_O1_conf *)
-lemma lsuba_drops_conf_isuni: ∀G,L1,L2. G ⊢ L1 ⫃⁝ L2 →
- ∀b,f,K1. 𝐔⦃f⦄ → ⬇*[b, f] L1 ≘ K1 →
- ∃∃K2. G ⊢ K1 ⫃⁝ K2 & ⬇*[b, f] L2 ≘ K2.
-#G #L1 #L2 #H elim H -L1 -L2
-[ /2 width=3 by ex2_intro/
-| #I #L1 #L2 #HL12 #IH #b #f #K1 #Hf #H
- elim (drops_inv_bind1_isuni … Hf H) -Hf -H *
- [ #Hf #H destruct -IH
- /3 width=3 by lsuba_bind, drops_refl, ex2_intro/
- | #g #Hg #HLK1 #H destruct -HL12
- elim (IH … Hg HLK1) -L1 -Hg /3 width=3 by drops_drop, ex2_intro/
- ]
-| #L1 #L2 #W #V #A #HV #HW #HL12 #IH #b #f #K1 #Hf #H
- elim (drops_inv_bind1_isuni … Hf H) -Hf -H *
- [ #Hf #H destruct -IH
- /3 width=3 by drops_refl, lsuba_beta, ex2_intro/
- | #g #Hg #HLK1 #H destruct -HL12
- elim (IH … Hg HLK1) -L1 -Hg /3 width=3 by drops_drop, ex2_intro/
- ]
-]
-qed-.
-
-(* Note: the premise 𝐔⦃f⦄ cannot be removed *)
-(* Basic_2A1: includes: lsuba_drop_O1_trans *)
-lemma lsuba_drops_trans_isuni: ∀G,L1,L2. G ⊢ L1 ⫃⁝ L2 →
- ∀b,f,K2. 𝐔⦃f⦄ → ⬇*[b, f] L2 ≘ K2 →
- ∃∃K1. G ⊢ K1 ⫃⁝ K2 & ⬇*[b, f] L1 ≘ K1.
-#G #L1 #L2 #H elim H -L1 -L2
-[ /2 width=3 by ex2_intro/
-| #I #L1 #L2 #HL12 #IH #b #f #K2 #Hf #H
- elim (drops_inv_bind1_isuni … Hf H) -Hf -H *
- [ #Hf #H destruct -IH
- /3 width=3 by lsuba_bind, drops_refl, ex2_intro/
- | #g #Hg #HLK2 #H destruct -HL12
- elim (IH … Hg HLK2) -L2 -Hg /3 width=3 by drops_drop, ex2_intro/
- ]
-| #L1 #L2 #W #V #A #HV #HW #HL12 #IH #b #f #K2 #Hf #H
- elim (drops_inv_bind1_isuni … Hf H) -Hf -H *
- [ #Hf #H destruct -IH
- /3 width=3 by drops_refl, lsuba_beta, ex2_intro/
- | #g #Hg #HLK2 #H destruct -HL12
- elim (IH … Hg HLK2) -L2 -Hg /3 width=3 by drops_drop, ex2_intro/
- ]
-]
-qed-.