+++ /dev/null
-(**************************************************************************)
-(* ___ *)
-(* ||M|| *)
-(* ||A|| A project by Andrea Asperti *)
-(* ||T|| *)
-(* ||I|| Developers: *)
-(* ||T|| The HELM team. *)
-(* ||A|| http://helm.cs.unibo.it *)
-(* \ / *)
-(* \ / This file is distributed under the terms of the *)
-(* v GNU General Public License Version 2 *)
-(* *)
-(**************************************************************************)
-
-include "basic_2/rt_computation/csx_lsubr.ma".
-include "basic_2/rt_computation/csx_cpxs.ma".
-include "basic_2/rt_computation/lsubsx_rdsx.ma".
-
-(* STRONGLY NORMALIZING REFERRED LOCAL ENV.S FOR UNBOUND RT-TRANSITION ******)
-
-(* Advanced properties ******************************************************)
-
-(* Basic_2A1: uses: lsx_lref_be_lpxs *)
-lemma rdsx_pair_lpxs (h) (o) (G):
- ∀K1,V. ⦃G, K1⦄ ⊢ ⬈*[h, o] 𝐒⦃V⦄ →
- ∀K2. G ⊢ ⬈*[h, o, V] 𝐒⦃K2⦄ → ⦃G, K1⦄ ⊢ ⬈*[h] K2 →
- ∀I. G ⊢ ⬈*[h, o, #0] 𝐒⦃K2.ⓑ{I}V⦄.
-#h #o #G #K1 #V #H
-@(csx_ind_cpxs … H) -V #V0 #_ #IHV0 #K2 #H
-@(rdsx_ind … H) -K2 #K0 #HK0 #IHK0 #HK10 #I
-@rdsx_intro #Y #HY #HnY
-elim (lpx_inv_pair_sn … HY) -HY #K2 #V2 #HK02 #HV02 #H destruct
-elim (tdeq_dec h o V0 V2) #HnV02 destruct [ -IHV0 -HV02 -HK0 | -IHK0 -HnY ]
-[ /5 width=5 by rdsx_rdeq_trans, lpxs_step_dx, rdeq_pair/
-| @(IHV0 … HnV02) -IHV0 -HnV02
- [ /2 width=3 by lpxs_cpx_trans/
- | /3 width=3 by rdsx_lpx_trans, rdsx_cpx_trans/
- | /2 width=3 by lpxs_step_dx/
- ]
-]
-qed.
-
-(* Basic_2A1: uses: lsx_lref_be *)
-lemma rdsx_lref_pair_drops (h) (o) (G):
- ∀K,V. ⦃G, K⦄ ⊢ ⬈*[h, o] 𝐒⦃V⦄ → G ⊢ ⬈*[h, o, V] 𝐒⦃K⦄ →
- ∀I,i,L. ⬇*[i] L ≘ K.ⓑ{I}V → G ⊢ ⬈*[h, o, #i] 𝐒⦃L⦄.
-#h #o #G #K #V #HV #HK #I #i elim i -i
-[ #L #H >(drops_fwd_isid … H) -H /2 width=3 by rdsx_pair_lpxs/
-| #i #IH #L #H
- elim (drops_inv_bind2_isuni_next … H) -H // #J #Y #HY #H destruct
- @(rdsx_lifts … (𝐔❴1❵)) /3 width=6 by drops_refl, drops_drop/ (**) (* full auto fails *)
-]
-qed.
-
-(* Main properties **********************************************************)
-
-(* Basic_2A1: uses: csx_lsx *)
-theorem csx_rdsx (h) (o): ∀G,L,T. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃T⦄ → G ⊢ ⬈*[h, o, T] 𝐒⦃L⦄.
-#h #o #G #L #T @(fqup_wf_ind_eq (Ⓕ) … G L T) -G -L -T
-#Z #Y #X #IH #G #L * * //
-[ #i #HG #HL #HT #H destruct
- elim (csx_inv_lref … H) -H [ |*: * ]
- [ /2 width=1 by rdsx_lref_atom/
- | /2 width=3 by rdsx_lref_unit/
- | /4 width=6 by rdsx_lref_pair_drops, fqup_lref/
- ]
-| #p #I #V #T #HG #HL #HT #H destruct
- elim (csx_fwd_bind_unit … H Void) -H /3 width=1 by rdsx_bind_void/
-| #I #V #T #HG #HL #HT #H destruct
- elim (csx_fwd_flat … H) -H /3 width=1 by rdsx_flat/
-]
-qed.