partial update update in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / rt_computation / lfpxs_cpxs.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lfpxs_cpxs.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lfpxs_cpxs.ma
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--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lfpxs_cpxs.ma
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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 "basic_2/rt_computation/cpxs_lfpx.ma".
-include "basic_2/rt_computation/lfpxs_fqup.ma".
-
-(* UNBOUND PARALLEL RT-COMPUTATION FOR LOCAL ENV.S ON REFERRED ENTRIES ******)
-
-(* Properties with unbound context-sensitive rt-computation for terms *******)
-
-(* Basic_2A1: uses: lpxs_pair lpxs_pair_refl *)
-lemma lfpxs_pair_refl: ∀h,G,L,V1,V2. ⦃G, L⦄ ⊢ V1 ⬈*[h] V2 →
-                       ∀I,T. ⦃G, L.ⓑ{I}V1⦄ ⊢ ⬈*[h, T] L.ⓑ{I}V2.
-/2 width=1 by tc_lfxs_pair_refl/ qed.
-
-lemma lfpxs_cpx_trans: ∀h,G. s_r_transitive … (cpx h G) (lfpxs h G).
-#h #G @s_r_trans_CTC2 @lfpx_cpxs_trans (**) (* auto fails *)
-qed-.
-
-(* Note: lfpxs_cpx_conf does not hold, thus we cannot invoke s_r_trans_CTC1 *)
-lemma lfpxs_cpxs_trans: ∀h,G. s_rs_transitive … (cpx h G) (lfpxs h G).
-#h #G @s_r_to_s_rs_trans @s_r_trans_CTC2
-@s_rs_trans_TC1 /2 width=3 by lfpx_cpxs_trans/ (**) (* full auto too slow *)
-qed-.
-
-(* Advanced properties on unbound rt-computation for terms ******************)
-
-lemma cpxs_bind2: ∀h,G,L,V1,V2. ⦃G, L⦄ ⊢ V1 ⬈*[h] V2 →
-                  ∀I,T1,T2. ⦃G, L.ⓑ{I}V2⦄ ⊢ T1 ⬈*[h] T2 →
-                  ∀p. ⦃G, L⦄ ⊢ ⓑ{p,I}V1.T1 ⬈*[h] ⓑ{p,I}V2.T2.
-/4 width=3 by lfpxs_cpxs_trans, lfpxs_pair_refl, cpxs_bind/ qed.
-
-(* Advanced inversion lemmas on unbound rt-computation for terms ************)
-
-lemma cpxs_inv_abst1: ∀h,p,G,L,V1,T1,U2. ⦃G, L⦄ ⊢ ⓛ{p}V1.T1 ⬈*[h] U2 →
-                      ∃∃V2,T2. ⦃G, L⦄ ⊢ V1 ⬈*[h] V2 & ⦃G, L.ⓛV1⦄ ⊢ T1 ⬈*[h] T2 &
-                               U2 = ⓛ{p}V2.T2.
-#h #p #G #L #V1 #T1 #U2 #H @(cpxs_ind … H) -U2 /2 width=5 by ex3_2_intro/
-#U0 #U2 #_ #HU02 * #V0 #T0 #HV10 #HT10 #H destruct
-elim (cpx_inv_abst1 … HU02) -HU02 #V2 #T2 #HV02 #HT02 #H destruct
-lapply (lfpxs_cpx_trans … HT02 (L.ⓛV1) ?)
-/3 width=5 by lfpxs_pair_refl, cpxs_trans, cpxs_strap1, ex3_2_intro/
-qed-.
-
-lemma cpxs_inv_abbr1: ∀h,p,G,L,V1,T1,U2. ⦃G, L⦄ ⊢ ⓓ{p}V1.T1 ⬈*[h] U2 → (
-                      ∃∃V2,T2. ⦃G, L⦄ ⊢ V1 ⬈*[h] V2 & ⦃G, L.ⓓV1⦄ ⊢ T1 ⬈*[h] T2 &
-                               U2 = ⓓ{p}V2.T2
-                      ) ∨
-                      ∃∃T2. ⦃G, L.ⓓV1⦄ ⊢ T1 ⬈*[h] T2 & ⬆*[1] U2 ≘ T2 & p = true.
-#h #p #G #L #V1 #T1 #U2 #H @(cpxs_ind … H) -U2 /3 width=5 by ex3_2_intro, or_introl/
-#U0 #U2 #_ #HU02 * *
-[ #V0 #T0 #HV10 #HT10 #H destruct
-  elim (cpx_inv_abbr1 … HU02) -HU02 *
-  [ #V2 #T2 #HV02 #HT02 #H destruct
-    lapply (lfpxs_cpx_trans … HT02 (L.ⓓV1) ?)
-    /4 width=5 by lfpxs_pair_refl, cpxs_trans, cpxs_strap1, ex3_2_intro, or_introl/
-  | #T2 #HT02 #HUT2
-    lapply (lfpxs_cpx_trans … HT02 (L.ⓓV1) ?) -HT02
-    /4 width=3 by lfpxs_pair_refl, cpxs_trans, ex3_intro, or_intror/
-  ]
-| #U1 #HTU1 #HU01
-  elim (cpx_lifts_sn … HU02 (Ⓣ) … (L.ⓓV1) … HU01)
-  /4 width=3 by cpxs_strap1, drops_refl, drops_drop, ex3_intro, or_intror/
-]
-qed-.