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

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   3 (*      ||M||                                                             *)
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  14
  15 include "static_2/static/rdeq_fqup.ma".
  16 include "basic_2/rt_transition/cwhx.ma".
  17
  18 (* WHD NORMAL TERMS FOR UNBOUND CONTEXT-SENSITIVE PARALLEL RT-TRANSITION ****)
  19
  20 (* Properties with sort-irrelevant equivalence ******************************)
  21
  22 lemma rdeq_tdeq_cwhx_trans (h) (G):
  23                            ∀L2,T2. ⦃G,L2⦄ ⊢ ⬈[h] 𝐖𝐇⦃T2⦄ →
  24                            ∀T1. T1 ≛ T2 →
  25                            ∀L1. L1 ≛[T1] L2 → ⦃G,L1⦄ ⊢ ⬈[h] 𝐖𝐇⦃T1⦄.
  26 #h #G #L2 #T2 #H elim H -L2 -T2
  27 [ #L2 #s2 #X1 #HX #L1 #HL
  28   elim (tdeq_inv_sort2 … HX) -HX #s1 #H destruct -s2 //
  29 | #p #L2 #W2 #T2 #X1 #HX #L1 #HL
  30   elim (tdeq_inv_pair2 … HX) -HX #W1 #T1 #_ #_ #H destruct -W2 -T2 //
  31 | #L2 #V2 #T2 #_ #IH #X1 #HX #L1 #HL
  32   elim (tdeq_inv_pair2 … HX) -HX #V1 #T1 #HV12 #HT12 #H destruct
  33   elim (rdeq_inv_bind … HL) -HL #HV1 #HT1
  34   /5 width=2 by cwhx_ldef, rdeq_bind_repl_dx, ext2_pair/
  35 ]
  36 qed-.
  37
  38 lemma tdeq_cwhx_trans (h) (G) (L):
  39                       ∀T2. ⦃G,L⦄ ⊢ ⬈[h] 𝐖𝐇⦃T2⦄ →
  40                       ∀T1. T1 ≛ T2 → ⦃G,L⦄ ⊢ ⬈[h] 𝐖𝐇⦃T1⦄.
  41 /3 width=5 by rdeq_tdeq_cwhx_trans/ qed-.