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4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
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15 include "basic_2/rt_computation/csx_lsubr.ma".
16 include "basic_2/rt_computation/csx_cpxs.ma".
17 include "basic_2/rt_computation/sdsx_rdsx.ma".
19 (* STRONGLY NORMALIZING REFERRED LOCAL ENV.S FOR UNBOUND RT-TRANSITION ******)
21 (* Advanced properties ******************************************************)
23 lemma rdsx_pair_lpxs (h) (I) (G):
24 ∀K1,V1. G ⊢ ⬈*[h,V1] 𝐒⦃K1⦄ →
25 ∀V2. ⦃G,K1⦄ ⊢ ⬈*[h] 𝐒⦃V2⦄ →
26 (∀K. ⦃G,K1⦄ ⊢ ⬈*[h] K → ⦃G,K⦄ ⊢ V1 ⬈*[h] V2) →
27 G ⊢ ⬈*[h,#0] 𝐒⦃K1.ⓑ{I}V2⦄.
29 @(rdsx_ind_lpxs … H) -K1 #K1 #_ #IHK #V2 #H
30 @(csx_ind_cpxs … H) -V2 #V2 #HV2 #IHV #HK
31 @rdsx_intro_lpxs #Y #HY #HnY
32 elim (lpxs_inv_pair_sn … HY) -HY #K3 #V3 #HK13 #HV23 #H destruct
35 @(rdsx_rdeq_trans … (K3.ⓑ{I}V2)) [| /2 width=1 by rdeq_pair_refl/ ]
39 | /3 width=3 by lpxs_trans/
42 @(rdsx_lpxs_trans … (K1.ⓑ{I}V3)) [| /2 width=1 by lpxs_bind_refl_dx/ ]
43 @(IHV … HV23 HnV23) -IHV -HnV23