- lambda_delta: programmed renaming to lambdadelta

[helm.git] / matita / matita / contribs / lambda_delta / basic_2 / substitution / lsubs_sfr.ma

diff --git a/matita/matita/contribs/lambda_delta/basic_2/substitution/lsubs_sfr.ma b/matita/matita/contribs/lambda_delta/basic_2/substitution/lsubs_sfr.ma
deleted file mode 100644 (file)
index b71f25e..0000000
--- a/matita/matita/contribs/lambda_delta/basic_2/substitution/lsubs_sfr.ma
+++ /dev/null
@@ -1,73 +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/substitution/lsubs.ma".
-
-(* LOCAL ENVIRONMENT REFINEMENT FOR SUBSTITUTION ****************************)
-
-(* bottom element of the refinement *)
-definition sfr: nat → nat → predicate lenv ≝
-   λd,e. NF_sn … (lsubs d e) (lsubs d e …).
-
-interpretation
-   "local environment full refinement (substitution)"
-   'SubEqBottom d e L = (sfr d e L).
-
-(* Basic properties *********************************************************)
-
-lemma sfr_atom: ∀d,e. ≽ [d, e] ⋆.
-#d #e #L #H
-elim (lsubs_inv_atom2 … H) -H
-[ #H destruct //
-| * #H1 #H2 destruct //
-]
-qed.
-
-lemma sfr_OO: ∀L. ≽ [0, 0] L.
-// qed.
-
-lemma sfr_abbr: ∀L,V,e. ≽ [0, e] L → ≽ [0, e + 1] L.ⓓV.
-#L #V #e #HL #K #H
-elim (lsubs_inv_abbr2 … H ?) -H // <minus_plus_m_m #X #HLX #H destruct
-lapply (HL … HLX) -HL -HLX /2 width=1/
-qed.
-
-lemma sfr_abbr_O: ∀L,V. ≽[0,1] L.ⓓV.
-#L #V
-@(sfr_abbr … 0) //
-qed.
-
-lemma sfr_skip: ∀I,L,V,d,e. ≽ [d, e] L → ≽ [d + 1, e] L.ⓑ{I}V.
-#I #L #V #d #e #HL #K #H
-elim (lsubs_inv_skip2 … H ?) -H // <minus_plus_m_m #J #X #W #HLX #H destruct
-lapply (HL … HLX) -HL -HLX /2 width=1/
-qed.
-
-(* Basic inversion lemmas ***************************************************)
-
-lemma sfr_inv_bind: ∀I,L,V,e. ≽ [0, e] L.ⓑ{I}V → 0 < e →
-                    ≽ [0, e - 1] L ∧ I = Abbr.
-#I #L #V #e #HL #He
-lapply (HL (L.ⓓV) ?) /2 width=1/ #H
-elim (lsubs_inv_abbr2 … H ?) -H // #K #_ #H destruct
-@conj // #L #HKL
-lapply (HL (L.ⓓV) ?) -HL /2 width=1/ -HKL #H
-elim (lsubs_inv_abbr2 … H ?) -H // -He #X #HLX #H destruct //
-qed-.
-
-lemma sfr_inv_skip: ∀I,L,V,d,e. ≽ [d, e] L.ⓑ{I}V → 0 < d → ≽ [d - 1, e] L.
-#I #L #V #d #e #HL #Hd #K #HLK
-lapply (HL (K.ⓑ{I}V) ?) -HL /2 width=1/ -HLK #H
-elim (lsubs_inv_skip2 … H ?) -H // -Hd #J #X #W #HKX #H destruct //
-qed-.