milestone update in ground_2 and basic_2A

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / etc_2A1 / fpn / fsb_alt.etc

diff --git a/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/fpn/fsb_alt.etc b/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/fpn/fsb_alt.etc
deleted file mode 100644 (file)
index 8c69a00..0000000
--- a/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/fpn/fsb_alt.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 "basic_2/notation/relations/btsnalt_5.ma".
-include "basic_2/computation/fpbs_fpbs.ma".
-include "basic_2/computation/fsb.ma".
-
-(* "BIG TREE" STRONGLY NORMALIZING TERMS ************************************)
-
-(* Note: alternative definition of fsb *)
-inductive fsba (h) (g): relation3 genv lenv term ≝
-| fsba_intro: ∀G1,L1,T1. (
-                 ∀G2,L2,T2. ⦃G1, L1, T1⦄ ≥[h, g] ⦃G2, L2, T2⦄ →
-                 (⦃G1, L1, T1⦄ ⋕ ⦃G2, L2, T2⦄ → ⊥) → fsba h g G2 L2 T2
-              ) → fsba h g G1 L1 T1.
-
-interpretation
-   "'big tree' strong normalization (closure) alternative"
-   'BTSNAlt h g G L T = (fsba h g G L T).
-
-(* Basic eliminators ********************************************************)
-
-theorem fsba_ind_alt: ∀h,g. ∀R: relation3 …. (
-                         ∀G1,L1,T1. ⦃G1, L1⦄ ⊢ ⦥⦥[h,g] T1 → (
-                            ∀G2,L2,T2. ⦃G1, L1, T1⦄ ≥[h, g] ⦃G2, L2, T2⦄ →
-                            (⦃G1, L1, T1⦄ ⋕ ⦃G2, L2, T2⦄ → ⊥) → R G2 L2 T2
-                         ) → R G1 L1 T1
-                      ) →
-                      ∀G,L,T. ⦃G, L⦄ ⊢ ⦥⦥[h, g] T → R G L T.
-#h #g #R #IH #G #L #T #H elim H -G -L -T
-/5 width=1 by fsba_intro/
-qed-.
-
-(* Basic_properties *********************************************************)
-
-fact fsba_intro_aux: ∀h,g,G1,L1,T1. (
-                        ∀G,G2,L,L2,T,T2. ⦃G, L, T⦄ ≥[h, g] ⦃G2, L2, T2⦄ →
-                        ⦃G1, L1, T1⦄ ⋕ ⦃G, L, T⦄ →
-                        (⦃G1, L1, T1⦄ ⋕ ⦃G2, L2, T2⦄ → ⊥) → fsba h g G2 L2 T2
-                     ) → fsba h g G1 L1 T1.
-/4 width=5 by fsba_intro/ qed-.
-
-lemma fsba_fpbs_trans: ∀h,g,G1,L1,T1. ⦃G1, L1⦄ ⊢ ⦥⦥[h, g] T1 →
-                       ∀G2,L2,T2. ⦃G1, L1, T1⦄ ≥[h, g] ⦃G2, L2, T2⦄ → ⦃G2, L2⦄ ⊢ ⦥⦥[h, g] T2.
-#h #g #G1 #L1 #T1 #H @(fsba_ind_alt … H) -G1 -L1 -T1
-#G1 #L1 #T1 #H0 #IH0 #G #L #T #H1 @fsba_intro
-#G2 #L2 #T2 #H2 #_ lapply (fpbs_trans … H1 … H2) -G -L -T
-#H12 elim (bteq_dec G1 G2 L1 L2 T1 T2) /3 width=6 by fpb_fpbs/
--IH0 #H212 
- 
-
- -H0 -H #H @(IH0 … H) -IH0 -H // @(fpbs_trans … H1 … H2)    
-
-lemma fsba_intro_fpb: ∀h,g,G1,L1,T1. (
-                         ∀G2,L2,T2. ⦃G1, L1, T1⦄ ≽[h, g] ⦃G2, L2, T2⦄ →
-                         (⦃G1, L1, T1⦄ ⋕ ⦃G2, L2, T2⦄ → ⊥) → ⦃G2, L2⦄ ⊢ ⦥⦥[h, g] T2
-                      ) → ⦃G1, L1⦄ ⊢ ⦥⦥[h, g] T1.
-#h #g #G1 #L1 #T1 #IH1 @fsba_intro_aux
-#G #G2 #L #L2 #T #T2 #H @(fpbs_ind_dx … H) -G -L -T
-[ #H1 #H2 -IH1 elim H2 -H2 //
-| #G0 #G #L0 #L #T0 #T #H10 #H12 #IH2 #H210 #H212 elim (bteq_dec G1 G L1 L T1 T) 
-  [ -IH1 -H210 -H10 -H12 /3 width=1 by/
-  | -IH2 -H212 #H21 lapply (IH1 … H21) -IH1 -H21
-    [
-    | -H10 -H210 #H 
-(*
-(* Main inversion lemmas ****************************************************)
-
-theorem fsba_inv_fsb: ∀h,g,G,L,T. ⦃G, L⦄ ⊢ ⦥⦥[h, g] T → ⦃G, L⦄ ⊢ ⦥[h, g] T.
-#h #g #G #L #T #H elim H -G -L -T
-/5 width=12 by fsb_intro, fpb_fpbs, fpbc_fwd_fpb, fpbc_fwd_gen/
-qed-.
-
-(* Main properties **********************************************************)
-
-theorem fsb_fsba: ∀h,g,G,L,T. ⦃G, L⦄ ⊢ ⦥[h, g] T → ⦃G, L⦄ ⊢ ⦥⦥[h, g] T.
-#h #g #G #L #T #H @(fsb_ind_alt … H) -G -L -T
-/4 width=1 by fsba_intro_fpb/
-qed.
-(*
-| fsba_intro: ∀G1,L1,T1. (
-                ∀G2,L2,T2.  ⦃G1, L1, T1⦄ ≻[h, g] ⦃G2, L2, T2⦄ → fsb h g G2 L2 T2
-              ) → fsb h g G1 L1 T1
-.
-
-
-
-(****************************************************************************)
-
-include "basic_2/substitution/fqup.ma".
-
-lemma fsb_csx: ∀h,g,G,L,T. ⦃G, L⦄ ⊢ ⬊*[h, g] T → ⦃G, L⦄ ⊢ ⦥[h, g] T.
-#h #g #G #L #T #H @(csx_ind … H) -T
-*)*)