property S2 of strongly normalizing terms proved!

[helm.git] / matita / matita / contribs / lambda_delta / basic_2 / computation / csn_lcpr_vector.ma

diff --git a/matita/matita/contribs/lambda_delta/basic_2/computation/csn_lcpr_vector.ma b/matita/matita/contribs/lambda_delta/basic_2/computation/csn_lcpr_vector.ma
deleted file mode 100644 (file)
index 5f5465b..0000000
--- a/matita/matita/contribs/lambda_delta/basic_2/computation/csn_lcpr_vector.ma
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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/computation/acp_cr.ma".
-include "basic_2/computation/cprs_tstc_vector.ma".
-include "basic_2/computation/csn_lcpr.ma".
-include "basic_2/computation/csn_vector.ma".
-
-(* CONTEXT-SENSITIVE STRONGLY NORMALIZING TERM VECTORS **********************)
-
-(* Advanced properties ******************************************************)
-(*
-(* Basic_1: was only: sn3_appl_appls *)
-lemma csn_appl_appls_simple_tstc: ∀L,Vs,V,T1. L ⊢ ⬇* V → L ⊢ ⬇* T1 →
-                                  (∀T2. L ⊢ ⒶVs.T1 ➡* T2 → (ⒶVs.T1 ≃ T2 → False) → L ⊢ ⬇* ⓐV. T2) →
-                                  𝐒[T1] → L ⊢ ⬇* ⓐV. ⒶVs. T1.
-#L *
-[ #V #T1 #HV
-  @csn_appl_simple_tstc //
-| #V0 #Vs #V #T1 #HV #H1T1 #H2T1 #H3T1
-  @csn_appl_simple_tstc // -HV
-  [ @H2T1
-]
-qed.
-*)
-(* Basic_1: was: sn3_appls_beta *)
-lemma csn_applv_beta: ∀L,W. L ⊢ ⬇* W →
-                      ∀Vs,V,T. L ⊢ ⬇* ⒶVs.ⓓV.T →
-                      L ⊢ ⬇* ⒶVs. ⓐV.ⓛW. T.
-#L #W #HW #Vs elim Vs -Vs /2 width=1/ -HW
-#V0 #Vs #IHV #V #T #H1T
-lapply (csn_fwd_pair_sn … H1T) #HV0
-lapply (csn_fwd_flat_dx … H1T) #H2T
-@csn_appl_simple_tstc // -HV0 /2 width=1/ -IHV -H2T
-[ #X #H #H0
-  elim (cprs_fwd_beta_vector … H) -H #H
-  [ -H1T elim (H0 ?) -H0 //
-  | -H0 @(csn_cprs_trans … H1T) -H1T /2 width=1/
-  ]
-| -H1T elim Vs -Vs //
-]
-qed.
-
-lemma csn_applv_delta: ∀L,K,V1,i. ⇩[0, i] L ≡ K. ⓓV1 →
-                       ∀V2. ⇧[0, i + 1] V1 ≡ V2 →
-                       ∀Vs.L ⊢ ⬇* (ⒶVs. V2) → L ⊢ ⬇* (ⒶVs. #i).
-#L #K #V1 #i #HLK #V2 #HV12 #Vs elim Vs -Vs
-[ #H
-  lapply (ldrop_fwd_ldrop2 … HLK) #HLK0
-  lapply (csn_inv_lift … H … HLK0 HV12) -V2 -HLK0 /2 width=4/
-| #V #Vs #IHV #H1T
-  lapply (csn_fwd_pair_sn … H1T) #HV
-  lapply (csn_fwd_flat_dx … H1T) #H2T
-  @csn_appl_simple_tstc // -HV /2 width=1/ -IHV -H2T
-  [ #X #H #H0
-    elim (cprs_fwd_delta_vector … HLK … HV12 … H) -HLK -HV12 -H #H
-    [ -H1T elim (H0 ?) -H0 //
-    | -H0 @(csn_cprs_trans … H1T) -H1T /2 width=1/
-    ]
-  | -L -K -V -V1 -V2 elim Vs -Vs //
-  ]
-]
-qed.
-
-(* Basic_1: was: sn3_appls_abbr *) 
-lemma csn_applv_theta: ∀L,V1s,V2s. ⇧[0, 1] V1s ≡ V2s →
-                       ∀V,T. L ⊢ ⬇* ⓓV. ⒶV2s. T → L ⊢ ⬇* V →
-                       L ⊢ ⬇* ⒶV1s. ⓓV. T.
-#L #V1s #V2s * -V1s -V2s /2 width=1/
-#V1s #V2s #V1 #V2 #HV12 #H 
-generalize in match HV12; -HV12 generalize in match V2; -V2 generalize in match V1; -V1
-elim H -V1s -V2s /2 width=3/
-#V1s #V2s #V1 #V2 #HV12 #HV12s #IHV12s #W1 #W2 #HW12 #V #T #H #HV
-lapply (csn_appl_theta … HW12 … H) -H -HW12 #H
-lapply (csn_fwd_pair_sn … H) #HW1
-lapply (csn_fwd_flat_dx … H) #H1
-@csn_appl_simple_tstc // -HW1 /2 width=3/ -IHV12s -HV -H1 #X #H1 #H2
-elim (cprs_fwd_theta_vector … (V2::V2s) … H1) -H1 /2 width=1/ -HV12s -HV12
-[ -H #H elim (H2 ?) -H2 //
-| -H2 #H1 @(csn_cprs_trans … H) -H /2 width=1/
-]
-qed.
-
-(* Basic_1: was: sn3_appls_cast *)
-lemma csn_applv_tau: ∀L,W. L ⊢ ⬇* W →
-                     ∀Vs,T. L ⊢ ⬇* ⒶVs. T →
-                     L ⊢ ⬇* ⒶVs. ⓣW. T.
-#L #W #HW #Vs elim Vs -Vs /2 width=1/ -HW
-#V #Vs #IHV #T #H1T
-lapply (csn_fwd_pair_sn … H1T) #HV
-lapply (csn_fwd_flat_dx … H1T) #H2T
-@csn_appl_simple_tstc // -HV /2 width=1/ -IHV -H2T
-[ #X #H #H0
-  elim (cprs_fwd_tau_vector … H) -H #H
-  [ -H1T elim (H0 ?) -H0 //
-  | -H0 @(csn_cprs_trans … H1T) -H1T /2 width=1/
-  ]
-| -H1T elim Vs -Vs //
-]
-qed.
-(*
-theorem csn_acr: acr cpr (eq …) (csn …) (λL,T. L ⊢ ⬇* T).
-@mk_acr //
-[
-| /2 width=1/
-| /2 width=6/
-| #L #V1 #V2 #HV12 #V #T #H #HVT
-  @(csn_applv_theta … HV12) -HV12 //
-  @(csn_abbr) //
-| /2 width=1/
-| @csn_lift
-]
-qed.
-*)
-axiom csn_acr: acr cpr (eq …) (csn …) (λL,T. L ⊢ ⬇* T).