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4 (* ||A|| A project by Andrea Asperti *)
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15 include "basic_2/rt_transition/cpx_rdeq.ma".
16 include "basic_2/rt_computation/csx_csx.ma".
18 (* STRONGLY NORMALIZING TERMS FOR UNBOUND PARALLEL RT-TRANSITION ************)
20 (* Properties with degree-based equivalence for local environments **********)
22 (* Basic_2A1: uses: csx_lleq_conf *)
23 lemma csx_rdeq_conf: ∀h,o,G,L1,T. ⦃G, L1⦄ ⊢ ⬈*[h, o] 𝐒⦃T⦄ →
24 ∀L2. L1 ≛[h, o, T] L2 → ⦃G, L2⦄ ⊢ ⬈*[h, o] 𝐒⦃T⦄.
26 @(csx_ind … H) -T #T1 #_ #IH #L2 #HL12
27 @csx_intro #T2 #HT12 #HnT12
28 elim (rdeq_cpx_trans … HL12 … HT12) -HT12
29 /5 width=4 by cpx_rdeq_conf_sn, csx_tdeq_trans, tdeq_trans/
32 (* Basic_2A1: uses: csx_lleq_conf *)
33 lemma csx_rdeq_trans: ∀h,o,L1,L2,T. L1 ≛[h, o, T] L2 →
34 ∀G. ⦃G, L2⦄ ⊢ ⬈*[h, o] 𝐒⦃T⦄ → ⦃G, L1⦄ ⊢ ⬈*[h, o] 𝐒⦃T⦄.
35 /3 width=3 by csx_rdeq_conf, rdeq_sym/ qed-.