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4 (* ||A|| A project by Andrea Asperti *)
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7 (* ||T|| The HELM team. *)
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15 include "static_2/static/rdeq_req.ma".
16 include "basic_2/rt_transition/rpx_rdeq.ma".
17 include "basic_2/rt_transition/rpx_lpx.ma".
19 (* UNBOUND PARALLEL RT-TRANSITION FOR FULL LOCAL ENVIRONMENTS ***************)
21 (* Properties with degree-based equivalence for local environments **********)
23 (* Basic_2A1: uses: lleq_lpx_trans *)
24 lemma rdeq_lpx_trans (h) (o) (G): ∀L2,K2. ⦃G, L2⦄ ⊢ ⬈[h] K2 →
25 ∀L1. ∀T:term. L1 ≛[h, o, T] L2 →
26 ∃∃K1. ⦃G, L1⦄ ⊢ ⬈[h] K1 & K1 ≛[h, o, T] K2.
27 #h #o #G #L2 #K2 #HLK2 #L1 #T #HL12
28 lapply (lpx_rpx … T HLK2) -HLK2 #HLK2
29 elim (rdeq_rpx_trans … HLK2 … HL12) -L2 #K #H #HK2
30 elim (rpx_inv_lpx_req … H) -H #K1 #HLK1 #HK1
31 /3 width=5 by req_rdeq_trans, ex2_intro/