- strongly normalizing terms form a candidate of reducibility

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / rt_computation / csx_theq_vector.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_theq_vector.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_theq_vector.ma
deleted file mode 100644 (file)
index 55146e3..0000000
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_theq_vector.ma
+++ /dev/null
@@ -1,107 +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/computation/gcp_cr.ma".
-*)
-include "basic_2/rt_computation/cpxs_theq_vector.ma".
-include "basic_2/rt_computation/csx_vector.ma".
-include "basic_2/rt_computation/csx_theq.ma".
-include "basic_2/rt_computation/csx_lfpx.ma".
-
-(* STRONGLY NORMALIZING TERMS FOR UNCOUNTED PARALLEL RT-TRANSITION **********)
-
-(* Vector form of properties with head equivalence for terms ****************)
-(*
-*)
-(*
-*)
-
-(* Basic_1: was just: sn3_appls_beta *)
-lemma csx_applv_beta: ∀h,o,p,G,L,Vs,V,W,T. ⦃G, L⦄ ⊢ ⬈*[h, o] ⒶVs.ⓓ{p}ⓝW.V.T →
-                      ⦃G, L⦄ ⊢ ⬈*[h, o] ⒶVs. ⓐV.ⓛ{p}W.T.
-#h #o #a #G #L #Vs elim Vs -Vs /2 width=1 by csx_appl_beta/
-#V0 #Vs #IHV #V #W #T #H1T
-lapply (csx_fwd_pair_sn … H1T) #HV0
-lapply (csx_fwd_flat_dx … H1T) #H2T
-@csx_appl_simple_theq /2 width=1 by applv_simple, simple_flat/ -IHV -HV0 -H2T
-#X #H #H0
-elim (cpxs_fwd_beta_vector … H) -H #H
-[ -H1T elim H0 -H0 //
-| -H0 /3 width=5 by csx_cpxs_trans, cpxs_flat_dx/
-]
-qed.
-
-lemma csx_applv_delta: ∀h,o,I,G,L,K,V1,i. ⬇[i] L ≡ K.ⓑ{I}V1 →
-                       ∀V2. ⬆[0, i + 1] V1 ≡ V2 →
-                       ∀Vs. ⦃G, L⦄ ⊢ ⬈*[h, o] (ⒶVs.V2) → ⦃G, L⦄ ⊢ ⬈*[h, o] (ⒶVs.#i).
-#h #o #I #G #L #K #V1 #i #HLK #V2 #HV12 #Vs elim Vs -Vs
-[ /4 width=12 by csx_inv_lift, csx_lref_bind, drop_fwd_drop2/
-| #V #Vs #IHV #H1T
-  lapply (csx_fwd_pair_sn … H1T) #HV
-  lapply (csx_fwd_flat_dx … H1T) #H2T
-  @csx_appl_simple_theq /2 width=1 by applv_simple, simple_atom/ -IHV -HV  -H2T
-  #X #H #H0
-  elim (cpxs_fwd_delta_vector … HLK … HV12 … H) -HLK -HV12 -H #H
-  [ -H1T elim H0 -H0 //
-  | -H0 /3 width=5 by csx_cpxs_trans, cpxs_flat_dx/
-  ]
-]
-qed.
-
-(* Basic_1: was just: sn3_appls_abbr *)
-lemma csx_applv_theta: ∀h,o,a,G,L,V1b,V2b. ⬆[0, 1] V1b ≡ V2b →
-                       ∀V,T. ⦃G, L⦄ ⊢ ⬈*[h, o] ⓓ{a}V.ⒶV2b.T →
-                       ⦃G, L⦄ ⊢ ⬈*[h, o] ⒶV1b.ⓓ{a}V.T.
-#h #o #a #G #L #V1b #V2b * -V1b -V2b /2 width=1 by/
-#V1b #V2b #V1 #V2 #HV12 #H
-generalize in match HV12; -HV12 generalize in match V2; -V2 generalize in match V1; -V1
-elim H -V1b -V2b /2 width=3 by csx_appl_theta/
-#V1b #V2b #V1 #V2 #HV12 #HV12b #IHV12b #W1 #W2 #HW12 #V #T #H
-lapply (csx_appl_theta … HW12 … H) -H -HW12 #H
-lapply (csx_fwd_pair_sn … H) #HW1
-lapply (csx_fwd_flat_dx … H) #H1
-@csx_appl_simple_theq /2 width=3 by simple_flat/ -IHV12b -HW1 -H1 #X #H1 #H2
-elim (cpxs_fwd_theta_vector … (V2@V2b) … H1) -H1 /2 width=1 by liftv_cons/ -HV12b -HV12
-[ -H #H elim H2 -H2 //
-| -H2 /3 width=5 by csx_cpxs_trans, cpxs_flat_dx/
-]
-qed.
-
-(* Basic_1: was just: sn3_appls_cast *)
-lemma csx_applv_cast: ∀h,o,G,L,Vs,W,T. ⦃G, L⦄ ⊢ ⬈*[h, o] ⒶVs.W → ⦃G, L⦄ ⊢ ⬈*[h, o] ⒶVs.T →
-                      ⦃G, L⦄ ⊢ ⬈*[h, o] ⒶVs.ⓝW.T.
-#h #o #G #L #Vs elim Vs -Vs /2 width=1 by csx_cast/
-#V #Vs #IHV #W #T #H1W #H1T
-lapply (csx_fwd_pair_sn … H1W) #HV
-lapply (csx_fwd_flat_dx … H1W) #H2W
-lapply (csx_fwd_flat_dx … H1T) #H2T
-@csx_appl_simple_theq /2 width=1 by applv_simple, simple_flat/ -IHV -HV -H2W -H2T
-#X #H #H0
-elim (cpxs_fwd_cast_vector … H) -H #H
-[ -H1W -H1T elim H0 -H0 //
-| -H1W -H0 /3 width=5 by csx_cpxs_trans, cpxs_flat_dx/
-| -H1T -H0 /3 width=5 by csx_cpxs_trans, cpxs_flat_dx/
-]
-qed.
-
-theorem csx_gcr: ∀h,o. gcr (cpx h o) (eq …) (csx h o) (csx h o).
-#h #o @mk_gcr //
-[ /3 width=1 by csx_applv_cnx/
-|2,3,6: /2 width=1 by csx_applv_beta, csx_applv_sort, csx_applv_cast/
-| /2 width=7 by csx_applv_delta/
-| #G #L #V1b #V2b #HV12b #a #V #T #H #HV
-  @(csx_applv_theta … HV12b) -HV12b
-  @csx_abbr //
-]
-qed.