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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/cpx_reqx.ma".
16 include "basic_2/rt_computation/csx_csx.ma".
18 (* STRONGLY NORMALIZING TERMS FOR UNBOUND PARALLEL RT-TRANSITION ************)
20 (* Properties with sort-irrelevant equivalence for local environments *******)
22 (* Basic_2A1: uses: csx_lleq_conf *)
23 lemma csx_reqx_conf: ∀h,G,L1,T. ❪G,L1❫ ⊢ ⬈*[h] 𝐒❪T❫ →
24 ∀L2. L1 ≛[T] L2 → ❪G,L2❫ ⊢ ⬈*[h] 𝐒❪T❫.
26 @(csx_ind … H) -T #T1 #_ #IH #L2 #HL12
27 @csx_intro #T2 #HT12 #HnT12
28 elim (reqx_cpx_trans … HL12 … HT12) -HT12
29 /5 width=5 by cpx_reqx_conf_sn, csx_teqx_trans, teqx_trans/
32 (* Basic_2A1: uses: csx_lleq_conf *)
33 lemma csx_reqx_trans: ∀h,L1,L2,T. L1 ≛[T] L2 →
34 ∀G. ❪G,L2❫ ⊢ ⬈*[h] 𝐒❪T❫ → ❪G,L1❫ ⊢ ⬈*[h] 𝐒❪T❫.
35 /3 width=3 by csx_reqx_conf, reqx_sym/ qed-.