- lambda_delta: programmed renaming to lambdadelta

[helm.git] / matita / matita / contribs / lambda_delta / basic_2 / reducibility / cnf.ma

diff --git a/matita/matita/contribs/lambda_delta/basic_2/reducibility/cnf.ma b/matita/matita/contribs/lambda_delta/basic_2/reducibility/cnf.ma
deleted file mode 100644 (file)
index 02bbcf8..0000000
--- a/matita/matita/contribs/lambda_delta/basic_2/reducibility/cnf.ma
+++ /dev/null
@@ -1,66 +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/reducibility/cpr.ma".
-
-(* CONTEXT-SENSITIVE NORMAL TERMS *******************************************)
-
-definition cnf: lenv → predicate term ≝ λL. NF … (cpr L) (eq …).
-
-interpretation
-   "context-sensitive normality (term)"
-   'Normal L T = (cnf L T).
-
-(* Basic inversion lemmas ***************************************************)
-
-lemma cnf_inv_appl: ∀L,V,T. L ⊢ 𝐍⦃ⓐV.T⦄ → ∧∧ L ⊢ 𝐍⦃V⦄ & L ⊢ 𝐍⦃T⦄ & 𝐒⦃T⦄.
-#L #V1 #T1 #HVT1 @and3_intro
-[ #V2 #HV2 lapply (HVT1 (ⓐV2.T1) ?) -HVT1 /2 width=1/ -HV2 #H destruct //
-| #T2 #HT2 lapply (HVT1 (ⓐV1.T2) ?) -HVT1 /2 width=1/ -HT2 #H destruct //
-| generalize in match HVT1; -HVT1 elim T1 -T1 * // #a * #W1 #U1 #_ #_ #H
-  [ elim (lift_total V1 0 1) #V2 #HV12
-    lapply (H (ⓓ{a}W1.ⓐV2.U1) ?) -H /3 width=3/ -HV12 #H destruct
-  | lapply (H (ⓓ{a}V1.U1) ?) -H /3 width=1/ #H destruct
-]
-qed-.
-
-lemma cnf_inv_zeta: ∀L,V,T. L ⊢ 𝐍⦃+ⓓV.T⦄ → ⊥.
-#L #V #T #H elim (is_lift_dec T 0 1)
-[ * #U #HTU
-  lapply (H U ?) -H /3 width=3 by cpr_tpr, tpr_zeta/ #H destruct (**) (* auto too slow without trace *)
-  elim (lift_inv_pair_xy_y … HTU)
-| #HT
-  elim (tps_full (⋆) V T (⋆. ⓓV) 0 ?) // #T2 #T1 #HT2 #HT12
-  lapply (H (+ⓓV.T2) ?) -H /3 width=3 by cpr_tpr, tpr_delta/ -HT2 #H destruct /3 width=2/ (**) (* auto too slow without trace *)
-]
-qed.
-
-lemma cnf_inv_tau: ∀L,V,T. L ⊢ 𝐍⦃ⓝV.T⦄ → ⊥.
-#L #V #T #H lapply (H T ?) -H /2 width=1/ #H
-@discr_tpair_xy_y //
-qed-.
-
-(* Basic properties *********************************************************)
-
-(* Basic_1: was: nf2_sort *)
-lemma cnf_sort: ∀L,k. L ⊢ 𝐍⦃⋆k⦄.
-#L #k #X #H
->(cpr_inv_sort1 … H) //
-qed.
-
-(* Basic_1: was: nf2_dec *)
-axiom cnf_dec: ∀L,T1. L ⊢ 𝐍⦃T1⦄ ∨
-               ∃∃T2. L ⊢ T1 ➡ T2 & (T1 = T2 → ⊥).
-
-(* Basic_1: removed theorems 1: nf2_abst_shift *)