milestone update in ground_2 and basic_2A

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / etc_2A1 / cpr / tpss_alt.etc

diff --git a/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/cpr/tpss_alt.etc b/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/cpr/tpss_alt.etc
deleted file mode 100644 (file)
index f7670ea..0000000
--- a/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/cpr/tpss_alt.etc
+++ /dev/null
@@ -1,105 +0,0 @@
-(**************************************************************************)
-(*       ___                                                              *)
-(*      ||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                  *)
-(*                                                                        *)
-(**************************************************************************)
-
-notation "hvbox( L ⊢ break term 46 T1 break ▶ ▶ * [ term 46 d , break term 46 e ] break term 46 T2 )"
-   non associative with precedence 45
-   for @{ 'PSubstStarAlt $L $T1 $d $e $T2 }.
-
-include "basic_2/unfold/tpss_lift.ma".
-
-(* PARALLEL UNFOLD ON TERMS *************************************************)
-
-(* alternative definition of tpss *)
-inductive tpssa: nat → nat → lenv → relation term ≝
-| tpssa_atom : ∀L,I,d,e. tpssa d e L (⓪{I}) (⓪{I})
-| tpssa_subst: ∀L,K,V1,V2,W2,i,d,e. d ≤ i → i < d + e →
-               ⇩[0, i] L ≡ K. ⓓV1 → tpssa 0 (d + e - i - 1) K V1 V2 →
-               ⇧[0, i + 1] V2 ≡ W2 → tpssa d e L (#i) W2
-| tpssa_bind : ∀L,a,I,V1,V2,T1,T2,d,e.
-               tpssa d e L V1 V2 → tpssa (d + 1) e (L. ⓑ{I} V2) T1 T2 →
-               tpssa d e L (ⓑ{a,I} V1. T1) (ⓑ{a,I} V2. T2)
-| tpssa_flat : ∀L,I,V1,V2,T1,T2,d,e.
-               tpssa d e L V1 V2 → tpssa d e L T1 T2 →
-               tpssa d e L (ⓕ{I} V1. T1) (ⓕ{I} V2. T2)
-.
-
-interpretation "parallel unfold (term) alternative"
-   'PSubstStarAlt L T1 d e T2 = (tpssa d e L T1 T2).
-
-(* Basic properties *********************************************************)
-
-lemma tpssa_lsubr_trans: ∀L1,T1,T2,d,e. L1 ⊢ T1 ▶▶* [d, e] T2 →
-                         ∀L2. L2 ⊑ [d, e] L1 → L2 ⊢ T1 ▶▶* [d, e] T2.
-#L1 #T1 #T2 #d #e #H elim H -L1 -T1 -T2 -d -e
-[ //
-| #L1 #K1 #V1 #V2 #W2 #i #d #e #Hdi #Hide #HLK1 #_ #HVW2 #IHV12 #L2 #HL12
-  elim (ldrop_lsubr_ldrop2_abbr … HL12 … HLK1 ? ?) -HL12 -HLK1 // /3 width=6/
-| /4 width=1/
-| /3 width=1/
-]
-qed.
-
-lemma tpssa_refl: ∀T,L,d,e. L ⊢ T ▶▶* [d, e] T.
-#T elim T -T //
-#I elim I -I /2 width=1/
-qed.
-
-lemma tpssa_tps_trans: ∀L,T1,T,d,e. L ⊢ T1 ▶▶* [d, e] T →
-                       ∀T2. L ⊢ T ▶ [d, e] T2 → L ⊢ T1 ▶▶* [d, e] T2.
-#L #T1 #T #d #e #H elim H -L -T1 -T -d -e
-[ #L #I #d #e #X #H
-  elim (tps_inv_atom1 … H) -H // * /2 width=6/
-| #L #K #V1 #V2 #W2 #i #d #e #Hdi #Hide #HLK #_ #HVW2 #IHV12 #T2 #H
-  lapply (ldrop_fwd_ldrop2 … HLK) #H0LK
-  lapply (tps_weak … H 0 (d+e) ? ?) -H // #H
-  elim (tps_inv_lift1_be … H … H0LK … HVW2 ? ?) -H -H0LK -HVW2 // /3 width=6/
-| #L #a #I #V1 #V #T1 #T #d #e #_ #_ #IHV1 #IHT1 #X #H
-  elim (tps_inv_bind1 … H) -H #V2 #T2 #HV2 #HT2 #H destruct
-  lapply (tps_lsubr_trans … HT2 (L.ⓑ{I}V) ?) -HT2 /2 width=1/ #HT2
-  lapply (IHV1 … HV2) -IHV1 -HV2 #HV12
-  lapply (IHT1 … HT2) -IHT1 -HT2 #HT12
-  lapply (tpssa_lsubr_trans … HT12 (L.ⓑ{I}V2) ?) -HT12 /2 width=1/
-| #L #I #V1 #V #T1 #T #d #e #_ #_ #IHV1 #IHT1 #X #H
-  elim (tps_inv_flat1 … H) -H #V2 #T2 #HV2 #HT2 #H destruct /3 width=1/
-]
-qed.
-
-lemma tpss_tpssa: ∀L,T1,T2,d,e. L ⊢ T1 ▶* [d, e] T2 → L ⊢ T1 ▶▶* [d, e] T2.
-#L #T1 #T2 #d #e #H @(tpss_ind … H) -T2 // /2 width=3/
-qed.
-
-(* Basic inversion lemmas ***************************************************)
-
-lemma tpssa_tpss: ∀L,T1,T2,d,e. L ⊢ T1 ▶▶* [d, e] T2 → L ⊢ T1 ▶* [d, e] T2.
-#L #T1 #T2 #d #e #H elim H -L -T1 -T2 -d -e // /2 width=6/
-qed-.
-
-lemma tpss_ind_alt: ∀R:nat→nat→lenv→relation term.
-                    (∀L,I,d,e. R d e L (⓪{I}) (⓪{I})) →
-                    (∀L,K,V1,V2,W2,i,d,e. d ≤ i → i < d + e →
-                     ⇩[O, i] L ≡ K.ⓓV1 → K ⊢ V1 ▶* [O, d + e - i - 1] V2 →
-                     ⇧[O, i + 1] V2 ≡ W2 → R O (d+e-i-1) K V1 V2 → R d e L (#i) W2
-                    ) →
-                    (∀L,a,I,V1,V2,T1,T2,d,e. L ⊢ V1 ▶* [d, e] V2 →
-                     L.ⓑ{I}V2 ⊢ T1 ▶* [d + 1, e] T2 → R d e L V1 V2 →
-                     R (d+1) e (L.ⓑ{I}V2) T1 T2 → R d e L (ⓑ{a,I}V1.T1) (ⓑ{a,I}V2.T2)
-                    ) →
-                    (∀L,I,V1,V2,T1,T2,d,e. L ⊢ V1 ▶* [d, e] V2 →
-                     L ⊢ T1 ▶* [d, e] T2 → R d e L V1 V2 →
-                     R d e L T1 T2 → R d e L (ⓕ{I}V1.T1) (ⓕ{I}V2.T2)
-                    ) →
-                    ∀d,e,L,T1,T2. L ⊢ T1 ▶* [d, e] T2 → R d e L T1 T2.
-#R #H1 #H2 #H3 #H4 #d #e #L #T1 #T2 #H elim (tpss_tpssa … H) -L -T1 -T2 -d -e
-// /3 width=1 by tpssa_tpss/ /3 width=7 by tpssa_tpss/
-qed-.