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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 "basic_2/rt_transition/lpx_rdeq.ma".
16 include "basic_2/rt_computation/rdsx.ma".
18 (* STRONGLY NORMALIZING REFERRED LOCAL ENV.S FOR UNBOUND RT-TRANSITION ******)
20 (* Advanced properties ******************************************************)
22 (* Basic_2A1: uses: lsx_lleq_trans *)
23 lemma rdsx_rdeq_trans (h) (o) (G):
24 ∀L1,T. G ⊢ ⬈*[h, o, T] 𝐒⦃L1⦄ →
25 ∀L2. L1 ≛[h, o, T] L2 → G ⊢ ⬈*[h, o, T] 𝐒⦃L2⦄.
26 #h #o #G #L1 #T #H @(rdsx_ind … H) -L1
27 #L1 #_ #IHL1 #L2 #HL12 @rdsx_intro
28 #L #HL2 #HnL2 elim (rdeq_lpx_trans … HL2 … HL12) -HL2
29 /4 width=5 by rdeq_repl/
32 (* Basic_2A1: uses: lsx_lpx_trans *)
33 lemma rdsx_lpx_trans (h) (o) (G):
34 ∀L1,T. G ⊢ ⬈*[h, o, T] 𝐒⦃L1⦄ →
35 ∀L2. ⦃G, L1⦄ ⊢ ⬈[h] L2 → G ⊢ ⬈*[h, o, T] 𝐒⦃L2⦄.
36 #h #o #G #L1 #T #H @(rdsx_ind … H) -L1 #L1 #HL1 #IHL1 #L2 #HL12
37 elim (rdeq_dec h o L1 L2 T) /3 width=4 by rdsx_rdeq_trans/