update in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / dynamic / snv.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv.ma
deleted file mode 100644 (file)
index a76beb8..0000000
--- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv.ma
+++ /dev/null
@@ -1,111 +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/notation/relations/nativevalid_5.ma".
-include "basic_2/computation/scpds.ma".
-
-(* STRATIFIED NATIVE VALIDITY FOR TERMS *************************************)
-
-(* activate genv *)
-inductive snv (h) (o): relation3 genv lenv term ≝
-| snv_sort: ∀G,L,s. snv h o G L (⋆s)
-| snv_lref: ∀I,G,L,K,V,i. ⬇[i] L ≘ K.ⓑ{I}V → snv h o G K V → snv h o G L (#i)
-| snv_bind: ∀a,I,G,L,V,T. snv h o G L V → snv h o G (L.ⓑ{I}V) T → snv h o G L (ⓑ{a,I}V.T)
-| snv_appl: ∀a,G,L,V,W0,T,U0,d. snv h o G L V → snv h o G L T →
-            ⦃G, L⦄ ⊢ V •*➡*[h, o, 1] W0 → ⦃G, L⦄ ⊢ T •*➡*[h, o, d] ⓛ{a}W0.U0 → snv h o G L (ⓐV.T)
-| snv_cast: ∀G,L,U,T,U0. snv h o G L U → snv h o G L T →
-            ⦃G, L⦄ ⊢ U •*➡*[h, o, 0] U0 → ⦃G, L⦄ ⊢ T •*➡*[h, o, 1] U0 → snv h o G L (ⓝU.T)
-.
-
-interpretation "stratified native validity (term)"
-   'NativeValid h o G L T = (snv h o G L T).
-
-(* Basic inversion lemmas ***************************************************)
-
-fact snv_inv_lref_aux: ∀h,o,G,L,X. ⦃G, L⦄ ⊢ X ¡[h, o] → ∀i. X = #i →
-                       ∃∃I,K,V. ⬇[i] L ≘ K.ⓑ{I}V & ⦃G, K⦄ ⊢ V ¡[h, o].
-#h #o #G #L #X * -G -L -X
-[ #G #L #s #i #H destruct
-| #I #G #L #K #V #i0 #HLK #HV #i #H destruct /2 width=5 by ex2_3_intro/
-| #a #I #G #L #V #T #_ #_ #i #H destruct
-| #a #G #L #V #W0 #T #U0 #d #_ #_ #_ #_ #i #H destruct
-| #G #L #U #T #U0 #_ #_ #_ #_ #i #H destruct
-]
-qed-.
-
-lemma snv_inv_lref: ∀h,o,G,L,i. ⦃G, L⦄ ⊢ #i ¡[h, o] →
-                    ∃∃I,K,V. ⬇[i] L ≘ K.ⓑ{I}V & ⦃G, K⦄ ⊢ V ¡[h, o].
-/2 width=3 by snv_inv_lref_aux/ qed-.
-
-fact snv_inv_gref_aux: ∀h,o,G,L,X. ⦃G, L⦄ ⊢ X ¡[h, o] → ∀p. X = §p → ⊥.
-#h #o #G #L #X * -G -L -X
-[ #G #L #s #p #H destruct
-| #I #G #L #K #V #i #_ #_ #p #H destruct
-| #a #I #G #L #V #T #_ #_ #p #H destruct
-| #a #G #L #V #W0 #T #U0 #d #_ #_ #_ #_ #p #H destruct
-| #G #L #U #T #U0 #_ #_ #_ #_ #p #H destruct
-]
-qed-.
-
-lemma snv_inv_gref: ∀h,o,G,L,p. ⦃G, L⦄ ⊢ §p ¡[h, o] → ⊥.
-/2 width=8 by snv_inv_gref_aux/ qed-.
-
-fact snv_inv_bind_aux: ∀h,o,G,L,X. ⦃G, L⦄ ⊢ X ¡[h, o] → ∀a,I,V,T. X = ⓑ{a,I}V.T →
-                       ⦃G, L⦄ ⊢ V ¡[h, o] ∧ ⦃G, L.ⓑ{I}V⦄ ⊢ T ¡[h, o].
-#h #o #G #L #X * -G -L -X
-[ #G #L #s #b #Z #X1 #X2 #H destruct
-| #I #G #L #K #V #i #_ #_ #b #Z #X1 #X2 #H destruct
-| #a #I #G #L #V #T #HV #HT #b #Z #X1 #X2 #H destruct /2 width=1 by conj/
-| #a #G #L #V #W0 #T #U0 #d #_ #_ #_ #_ #b #Z #X1 #X2 #H destruct
-| #G #L #U #T #U0 #_ #_ #_ #_ #b #Z #X1 #X2 #H destruct
-]
-qed-.
-
-lemma snv_inv_bind: ∀h,o,a,I,G,L,V,T. ⦃G, L⦄ ⊢ ⓑ{a,I}V.T ¡[h, o] →
-                    ⦃G, L⦄ ⊢ V ¡[h, o] ∧ ⦃G, L.ⓑ{I}V⦄ ⊢ T ¡[h, o].
-/2 width=4 by snv_inv_bind_aux/ qed-.
-
-fact snv_inv_appl_aux: ∀h,o,G,L,X. ⦃G, L⦄ ⊢ X ¡[h, o] → ∀V,T. X = ⓐV.T →
-                       ∃∃a,W0,U0,d. ⦃G, L⦄ ⊢ V ¡[h, o] & ⦃G, L⦄ ⊢ T ¡[h, o] &
-                                    ⦃G, L⦄ ⊢ V •*➡*[h, o, 1] W0 & ⦃G, L⦄ ⊢ T •*➡*[h, o, d] ⓛ{a}W0.U0.
-#h #o #G #L #X * -L -X
-[ #G #L #s #X1 #X2 #H destruct
-| #I #G #L #K #V #i #_ #_ #X1 #X2 #H destruct
-| #a #I #G #L #V #T #_ #_ #X1 #X2 #H destruct
-| #a #G #L #V #W0 #T #U0 #d #HV #HT #HVW0 #HTU0 #X1 #X2 #H destruct /2 width=6 by ex4_4_intro/
-| #G #L #U #T #U0 #_ #_ #_ #_ #X1 #X2 #H destruct
-]
-qed-.
-
-lemma snv_inv_appl: ∀h,o,G,L,V,T. ⦃G, L⦄ ⊢ ⓐV.T ¡[h, o] →
-                    ∃∃a,W0,U0,d. ⦃G, L⦄ ⊢ V ¡[h, o] & ⦃G, L⦄ ⊢ T ¡[h, o] &
-                                 ⦃G, L⦄ ⊢ V •*➡*[h, o, 1] W0 & ⦃G, L⦄ ⊢ T •*➡*[h, o, d] ⓛ{a}W0.U0.
-/2 width=3 by snv_inv_appl_aux/ qed-.
-
-fact snv_inv_cast_aux: ∀h,o,G,L,X. ⦃G, L⦄ ⊢ X ¡[h, o] → ∀U,T. X = ⓝU.T →
-                       ∃∃U0. ⦃G, L⦄ ⊢ U ¡[h, o] & ⦃G, L⦄ ⊢ T ¡[h, o] &
-                             ⦃G, L⦄ ⊢ U •*➡*[h, o, 0] U0 & ⦃G, L⦄ ⊢ T •*➡*[h, o, 1] U0.
-#h #o #G #L #X * -G -L -X
-[ #G #L #s #X1 #X2 #H destruct
-| #I #G #L #K #V #i #_ #_ #X1 #X2 #H destruct
-| #a #I #G #L #V #T #_ #_ #X1 #X2 #H destruct
-| #a #G #L #V #W0 #T #U0 #d #_ #_ #_ #_ #X1 #X2 #H destruct
-| #G #L #U #T #U0 #HV #HT #HU0 #HTU0 #X1 #X2 #H destruct /2 width=3 by ex4_intro/
-]
-qed-.
-
-lemma snv_inv_cast: ∀h,o,G,L,U,T. ⦃G, L⦄ ⊢ ⓝU.T ¡[h, o] →
-                    ∃∃U0. ⦃G, L⦄ ⊢ U ¡[h, o] & ⦃G, L⦄ ⊢ T ¡[h, o] &
-                          ⦃G, L⦄ ⊢ U •*➡*[h, o, 0] U0 & ⦃G, L⦄ ⊢ T •*➡*[h, o, 1] U0.
-/2 width=3 by snv_inv_cast_aux/ qed-.