refactoring to park the notions:

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / computation / lcosx.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/lcosx.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/lcosx.ma
deleted file mode 100644 (file)
index 8f29e1a..0000000
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/lcosx.ma
+++ /dev/null
@@ -1,77 +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                  *)
-(*                                                                        *)
-(**************************************************************************)
-
-include "basic_2/notation/relations/cosn_5.ma".
-include "basic_2/computation/lsx.ma".
-
-(* SN EXTENDED STRONGLY CONORMALIZING LOCAL ENVIRONMENTS ********************)
-
-inductive lcosx (h) (o) (G): relation2 ynat lenv ≝
-| lcosx_sort: ∀l. lcosx h o G l (⋆)
-| lcosx_skip: ∀I,L,T. lcosx h o G 0 L → lcosx h o G 0 (L.ⓑ{I}T)
-| lcosx_pair: ∀I,L,T,l. G ⊢ ⬊*[h, o, T, l] L →
-              lcosx h o G l L → lcosx h o G (⫯l) (L.ⓑ{I}T)
-.
-
-interpretation
-   "sn extended strong conormalization (local environment)"
-   'CoSN h o l G L = (lcosx h o G l L).
-
-(* Basic properties *********************************************************)
-
-lemma lcosx_O: ∀h,o,G,L. G ⊢ ~⬊*[h, o, 0] L.
-#h #o #G #L elim L /2 width=1 by lcosx_skip/
-qed.
-
-lemma lcosx_drop_trans_lt: ∀h,o,G,L,l. G ⊢ ~⬊*[h, o, l] L →
-                            ∀I,K,V,i. ⬇[i] L ≡ K.ⓑ{I}V → i < l →
-                            G ⊢ ~⬊*[h, o, ⫰(l-i)] K ∧ G ⊢ ⬊*[h, o, V, ⫰(l-i)] K.
-#h #o #G #L #l #H elim H -L -l
-[ #l #J #K #V #i #H elim (drop_inv_atom1 … H) -H #H destruct
-| #I #L #T #_ #_ #J #K #V #i #_ #H elim (ylt_yle_false … H) -H //
-| #I #L #T #l #HT #HL #IHL #J #K #V #i #H #Hil
-  elim (drop_inv_O1_pair1 … H) -H * #Hi #HLK destruct
-  [ >ypred_succ /2 width=1 by conj/
-  | lapply (ylt_pred … Hil ?) -Hil /2 width=1 by ylt_inj/ >ypred_succ #Hil
-    elim (IHL … HLK ?) -IHL -HLK <yminus_inj >yminus_SO2 //
-    <(ypred_succ l) in ⊢ (%→%→?); >yminus_pred /2 width=1 by ylt_inj, conj/
-  ]
-]
-qed-.
-
-(* Basic inversion lemmas ***************************************************)
-
-fact lcosx_inv_succ_aux: ∀h,o,G,L,x. G ⊢ ~⬊*[h, o, x] L → ∀l. x = ⫯l →
-                         L = ⋆ ∨
-                         ∃∃I,K,V. L = K.ⓑ{I}V & G ⊢ ~⬊*[h, o, l] K &
-                                  G ⊢ ⬊*[h, o, V, l] K.
-#h #o #G #L #l * -L -l /2 width=1 by or_introl/
-[ #I #L #T #_ #x #H elim (ysucc_inv_O_sn … H)
-| #I #L #T #l #HT #HL #x #H <(ysucc_inv_inj … H) -x
-  /3 width=6 by ex3_3_intro, or_intror/
-]
-qed-.
-
-lemma lcosx_inv_succ: ∀h,o,G,L,l. G ⊢ ~⬊*[h, o, ⫯l] L → L = ⋆ ∨
-                      ∃∃I,K,V. L = K.ⓑ{I}V & G ⊢ ~⬊*[h, o, l] K &
-                               G ⊢ ⬊*[h, o, V, l] K.
-/2 width=3 by lcosx_inv_succ_aux/ qed-.
-
-lemma lcosx_inv_pair: ∀h,o,I,G,L,T,l. G ⊢ ~⬊*[h, o, ⫯l] L.ⓑ{I}T →
-                      G ⊢ ~⬊*[h, o, l] L ∧ G ⊢ ⬊*[h, o, T, l] L.
-#h #o #I #G #L #T #l #H elim (lcosx_inv_succ … H) -H
-[ #H destruct
-| * #Z #Y #X #H destruct /2 width=1 by conj/
-]
-qed-.