more additions and corrections for the article

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / etc / sdsx / sdsx_rdsx.etc

diff --git a/matita/matita/contribs/lambdadelta/basic_2/etc/sdsx/sdsx_rdsx.etc b/matita/matita/contribs/lambdadelta/basic_2/etc/sdsx/sdsx_rdsx.etc
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+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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 "static_2/relocation/scl.ma".
+include "basic_2/rt_computation/rdsx_drops.ma".
+include "basic_2/rt_computation/rdsx_lpxs.ma".
+include "basic_2/rt_computation/sdsx.ma".
+
+axiom pippo (h) (f) (G) (V:term):
+      ∀L1. G ⊢ ⬈*[h,V] 𝐒⦃L1⦄ →
+      ∀L2. L1 ⊐ⓧ[f] L2 → G ⊢ ⬈*[h,V] 𝐒⦃L2⦄.
+
+
+(* STRONGLY NORMALIZING SELECTED LOCAL ENV.S FOR UNBOUND RT-TRANSITION ******)
+
+(* Properties with strongly normalizing referred local environments *********)
+
+(* Basic_2A1: uses: lsx_cpx_trans_lcosx *)
+lemma rdsx_cpx_trans_sdsx (h):
+      ∀G,L0,T1,T2. ⦃G,L0⦄ ⊢ T1 ⬈[h] T2 →
+      ∀f. G ⊢ ⬈*[h,f] 𝐒⦃L0⦄ → ∀L. L0 ⊐ⓧ[f] L →
+      G ⊢ ⬈*[h,T1] 𝐒⦃L⦄ → G ⊢ ⬈*[h,T2] 𝐒⦃L⦄.
+#h #G #L0 #T1 #T2 #H @(cpx_ind … H) -G -L0 -T1 -T2
+[ //
+| //
+| #I #G #K0 #V1 #V2 #W2 #_ #IH #HVW2 #g #H1 #Y #H2 #H3
+  elim (sdsx_inv_pair_gen … H1) -H1 *
+  [ #f #HK0 #H destruct
+    elim (scl_inv_push_sn … H2) -H2 #K #HK #H destruct
+    /4 width=8 by rdsx_lifts, rdsx_fwd_pair, drops_refl, drops_drop/
+  | #f #HV1 #HK0 #H destruct
+    elim (scl_inv_next_sn … H2) -H2 #K #HK #H destruct
+    /4 width=8 by pippo, rdsx_lifts, drops_refl, drops_drop/
+  ]
+| #I0 #G #K0 #T #U #i #_ #IH #HTU #g #H1 #Y #H2 #H3
+  lapply (sdsx_fwd_bind … H1) -H1 #HK0
+  elim (scl_fwd_bind_sn … H2) -H2 #I #K #HK #H destruct
+  /6 width=8 by rdsx_inv_lifts, rdsx_lifts, drops_refl, drops_drop/
+| #p #I #G #L0 #V1 #V2 #T1 #T2 #_ #_ #IHV12 #IHT12 #f #H1 #L #H2 #H3
+  elim (rdsx_inv_bind_void … H3) -H3 #HV1 #HT1
+  @rdsx_bind_void
+  [ /2 width=3 by/
+  | @(IHT12 (↑f) … HT1) 
+    [ @(sdsx_pair … H1) 
+    | /2 width=1 by scl_next/
+  
+  /4 width=2 by lsubsx_pair, rdsx_bind_void/
+| #I0 #G #L0 #V1 #V2 #T1 #T2 #_ #_ #IHV12 #IHT12 #f #L #HL0 #HL
+  elim (rdsx_inv_flat … HL) -HL /3 width=2 by rdsx_flat/
+| #G #L0 #V #U1 #T1 #T2 #HTU1 #_ #IHT12 #f #L #HL0 #HL
+  elim (rdsx_inv_bind … HL) -HL #HV #HU1
+  /5 width=8 by rdsx_inv_lifts, drops_refl, drops_drop/
+| #G #L0 #V #T1 #T2 #_ #IHT12 #f #L #HL0 #HL
+  elim (rdsx_inv_flat … HL) -HL /2 width=2 by/
+| #G #L0 #V1 #V2 #T #_ #IHV12 #f #L #HL0 #HL
+  elim (rdsx_inv_flat … HL) -HL /2 width=2 by/
+| #p #G #L0 #V1 #V2 #W1 #W2 #T1 #T2 #_ #_ #_ #IHV12 #IHW12 #IHT12 #f #L #HL0 #HL
+  elim (rdsx_inv_flat … HL) -HL #HV1 #HL
+  elim (rdsx_inv_bind … HL) -HL #HW1 #HT1
+  /4 width=2 by lsubsx_pair, rdsx_bind_void, rdsx_flat/
+| #p #G #L0 #V1 #V2 #U2 #W1 #W2 #T1 #T2 #_ #_ #_ #IHV12 #IHW12 #IHT12 #HVU2 #f #L #HL0 #HL
+  elim (rdsx_inv_flat … HL) -HL #HV1 #HL
+  elim (rdsx_inv_bind … HL) -HL #HW1 #HT1
+  /6 width=8 by lsubsx_pair, rdsx_lifts, rdsx_bind_void, rdsx_flat, drops_refl, drops_drop/
+]
+qed-.
+
+(* Advanced properties of strongly normalizing referred local environments **)
+
+(* Basic_2A1: uses: lsx_cpx_trans_O *)
+lemma rdsx_cpx_trans (h):
+      ∀G,L,T1,T2. ⦃G,L⦄ ⊢ T1 ⬈[h] T2 →
+      G ⊢ ⬈*[h,T1] 𝐒⦃L⦄ → G ⊢ ⬈*[h,T2] 𝐒⦃L⦄.
+/3 width=6 by rdsx_cpx_trans_lsubsx, lsubsx_refl/ qed-.
+
+lemma rdsx_cpxs_trans (h):
+      ∀G,L,T1,T2. ⦃G,L⦄ ⊢ T1 ⬈*[h] T2 →
+      G ⊢ ⬈*[h,T1] 𝐒⦃L⦄ → G ⊢ ⬈*[h,T2] 𝐒⦃L⦄.
+#h #G #L #T1 #T2 #H
+@(cpxs_ind_dx ???????? H) -T1 //
+/3 width=3 by rdsx_cpx_trans/
+qed-.
+*)