+++ /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/rt_transition/lpx_rdeq.ma".
-include "basic_2/rt_computation/lpxs_lpx.ma".
-
-(* UNBOUND PARALLEL RT-COMPUTATION FOR FULL LOCAL ENVIRONMENTS **************)
-
-(* Properties with sort-irrelevant equivalence on referred entries **********)
-
-(* Basic_2A1: uses: lleq_lpxs_trans *)
-lemma rdeq_lpxs_trans (h) (G) (T:term):
- ∀L2,K2. ⦃G,L2⦄ ⊢ ⬈*[h] K2 →
- ∀L1. L1 ≛[T] L2 →
- ∃∃K1. ⦃G,L1⦄ ⊢ ⬈*[h] K1 & K1 ≛[T] K2.
-#h #G #T #L2 #K2 #H @(lpxs_ind_sn … H) -L2 /2 width=3 by ex2_intro/
-#L #L2 #HL2 #_ #IH #L1 #HT
-elim (rdeq_lpx_trans … HL2 … HT) -L #L #HL1 #HT
-elim (IH … HT) -L2 #K #HLK #HT
-/3 width=3 by lpxs_step_sn, ex2_intro/
-qed-.
-
-(* Basic_2A1: uses: lpxs_nlleq_inv_step_sn *)
-lemma lpxs_rdneq_inv_step_sn (h) (G) (T:term):
- ∀L1,L2. ⦃G,L1⦄ ⊢ ⬈*[h] L2 → (L1 ≛[T] L2 → ⊥) →
- ∃∃L,L0. ⦃G,L1⦄ ⊢ ⬈[h] L & L1 ≛[T] L → ⊥ &
- ⦃G,L⦄ ⊢ ⬈*[h] L0 & L0 ≛[T] L2.
-#h #G #T #L1 #L2 #H @(lpxs_ind_sn … H) -L1
-[ #H elim H -H //
-| #L1 #L #H1 #H2 #IH2 #H12 elim (rdeq_dec L1 L T) #H
- [ -H1 -H2 elim IH2 -IH2 /3 width=3 by rdeq_trans/ -H12
- #L0 #L3 #H1 #H2 #H3 #H4 lapply (rdeq_rdneq_trans … H … H2) -H2
- #H2 elim (rdeq_lpx_trans … H1 … H) -L
- #L #H1 #H lapply (rdneq_rdeq_div … H … H2) -H2
- #H2 elim (rdeq_lpxs_trans … H3 … H) -L0
- /3 width=8 by rdeq_trans, ex4_2_intro/
- | -H12 -IH2 /3 width=6 by ex4_2_intro/
- ]
-]
-qed-.