- we introduce stratified term equivalence to remove the parameter g from cpx

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / etc / ssta1 / snv_aaa.etc

diff --git a/matita/matita/contribs/lambdadelta/basic_2/etc/ssta1/snv_aaa.etc b/matita/matita/contribs/lambdadelta/basic_2/etc/ssta1/snv_aaa.etc
deleted file mode 100644 (file)
index 20d72ef..0000000
--- a/matita/matita/contribs/lambdadelta/basic_2/etc/ssta1/snv_aaa.etc
+++ /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/computation/csx_aaa.ma".
-include "basic_2/computation/cpds_aaa.ma".
-include "basic_2/equivalence/cpcs_aaa.ma".
-include "basic_2/dynamic/snv.ma".
-
-(* STRATIFIED NATIVE VALIDITY FOR TERMS *************************************)
-
-(* Forward lemmas on atomic arity assignment for terms **********************)
-
-lemma snv_fwd_aaa: ∀h,g,G,L,T. ⦃G, L⦄ ⊢ T ¡[h, g] → ∃A. ⦃G, L⦄ ⊢ T ⁝ A.
-#h #g #G #L #T #H elim H -G -L -T
-[ /2 width=2/
-| #I #G #L #K #V #i #HLK #_ * /3 width=6/
-| #a * #G #L #V #T #_ #_ * #B #HV * #A #HA /3 width=2/
-| #a #G #L #V #W #W0 #T #U #l #_ #_ #Hl #HVW #HW0 #HTU * #B #HV * #X #HT
-  lapply (aaa_cpds_conf h g … HV W0 ?) [ -HTU /3 width=4/ ] -W #HW0 (**) (* auto fail without -HTU *)
-  lapply (aaa_cpds_conf … HT … HTU) -HTU #H
-  elim (aaa_inv_abst … H) -H #B0 #A #H1 #HU #H2 destruct
-  lapply (aaa_mono … H1 … HW0) -W0 #H destruct /3 width=4/
-| #G #L #W #T #U #l #_ #_ #_ #HTU #HUW * #B #HW * #A #HT
-  lapply (aaa_ssta_conf … HT … HTU) -HTU #H
-  lapply (aaa_cpcs_mono … HUW … H … HW) -HUW -H #H destruct /3 width=3/
-]
-qed-.
-
-lemma snv_fwd_csx: ∀h,g,G,L,T. ⦃G, L⦄ ⊢ T ¡[h, g] → ⦃G, L⦄ ⊢ ⬊*[h, g] T.
-#h #g #G #L #T #H elim (snv_fwd_aaa … H) -H /2 width=2/
-qed-.
-
-(* Advanced forward lemmas **************************************************)
-
-lemma snv_fwd_da: ∀h,g,G,L,T. ⦃G, L⦄ ⊢ T ¡[h, g] → ∃l. ⦃G, L⦄ ⊢ T ▪[h, g] l.
-#h #g #G #L #T #H elim (snv_fwd_aaa … H) -H /2 width=2 by aaa_fwd_da/
-qed-.
-
-lemma snv_fwd_ssta: ∀h,g,G,L,T. ⦃G, L⦄ ⊢ T ¡[h, g] → ∃U. ⦃G, L⦄ ⊢ T •[h, g] U.
-#h #g #G #L #T #H elim (snv_fwd_aaa … H) -H /2 width=2 by aaa_fwd_ssta/
-qed-.
-
-lemma snv_lsstas_fwd_correct: ∀h,g,G,L,T1,T2,l. ⦃G, L⦄ ⊢ T1 ¡[h, g] → ⦃G, L⦄ ⊢ T1 •* [h, g, l] T2 →
-                              ∃U2. ⦃G, L⦄ ⊢ T2 •[h, g] U2.
-#h #g #G #L #T1 #T2 #l #HT1 #HT12
-elim (snv_fwd_ssta … HT1) -HT1 /2 width=5 by lsstas_fwd_correct/
-qed-.
-
-(* Advanced properties ******************************************************)
-
-lemma snv_scast: ∀h,g,G,L,V,W,l. ⦃G, L⦄ ⊢ V ¡[h, g] → ⦃G, L⦄ ⊢ W ¡[h, g] →
-                 scast h g l G L V W → ⦃G, L⦄ ⊢V ▪[h, g] l+1 → ⦃G, L⦄ ⊢ ⓝW.V ¡[h, g].
-#h #g #G #L #V #W #l #HV #HW #H #Hl
-elim (snv_fwd_ssta … HV) /4 width=6 by snv_cast, ssta_lsstas/
-qed-.