matita/matita/contribs/lambdadelta/basic_2/rt_transition/lpx_rdeq.ma

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  14
  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".
  18
  19 (* UNBOUND PARALLEL RT-TRANSITION FOR FULL LOCAL ENVIRONMENTS ***************)
  20
  21 (* Properties with degree-based equivalence for local environments **********)
  22
  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/
  32 qed-.