update in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / etc / shnv / shnv.etc

diff --git a/matita/matita/contribs/lambdadelta/basic_2/etc/shnv/shnv.etc b/matita/matita/contribs/lambdadelta/basic_2/etc/shnv/shnv.etc
new file mode 100644 (file)
index 0000000..9616434
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/basic_2/etc/shnv/shnv.etc
@@ -0,0 +1,55 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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_6.ma".
+include "basic_2/equivalence/scpes.ma".
+include "basic_2/dynamic/snv.ma".
+
+(* STRATIFIED HIGHER NATIVE VALIDITY FOR TERMS ******************************)
+
+inductive shnv (h) (o) (d1) (G) (L): predicate term ≝
+| shnv_cast: ∀U,T. ⦃G, L⦄ ⊢ U ¡[h, o] → ⦃G, L⦄ ⊢ T ¡[h, o] →
+             (∀d2. d2 ≤ d1 → ⦃G, L⦄ ⊢ U •*⬌*[h, o, d2, d2+1] T) →
+             shnv h o d1 G L (ⓝU.T)
+.
+
+interpretation "stratified higher native validity (term)"
+   'NativeValid h o d G L T = (shnv h o d G L T).
+
+(* Basic inversion lemmas ***************************************************)
+
+fact shnv_inv_cast_aux: ∀h,o,G,L,X,d1. ⦃G, L⦄ ⊢ X ¡[h, o, d1] → ∀U,T. X = ⓝU.T →
+                        ∧∧ ⦃G, L⦄ ⊢ U ¡[h, o] & ⦃G, L⦄ ⊢ T ¡[h, o]
+                         & (∀d2. d2 ≤ d1 → ⦃G, L⦄ ⊢ U •*⬌*[h, o, d2, d2+1] T).
+#h #o #G #L #X #d1 * -X
+#U #T #HU #HT #HUT #U1 #T1 #H destruct /3 width=1 by and3_intro/
+qed-.
+
+lemma shnv_inv_cast: ∀h,o,G,L,U,T,d1. ⦃G, L⦄ ⊢ ⓝU.T ¡[h, o, d1] →
+                     ∧∧ ⦃G, L⦄ ⊢ U ¡[h, o] & ⦃G, L⦄ ⊢ T ¡[h, o]
+                      & (∀d2. d2 ≤ d1 → ⦃G, L⦄ ⊢ U •*⬌*[h, o, d2, d2+1] T).
+/2 width=3 by shnv_inv_cast_aux/ qed-.
+
+lemma shnv_inv_snv: ∀h,o,G,L,T,d. ⦃G, L⦄ ⊢ T ¡[h, o, d] → ⦃G, L⦄ ⊢ T ¡[h, o].
+#h #o #G #L #T #d * -T
+#U #T #HU #HT #HUT elim (HUT 0) -HUT /2 width=3 by snv_cast/
+qed-.
+
+(* Basic properties *********************************************************)
+
+lemma snv_shnv_cast: ∀h,o,G,L,U,T. ⦃G, L⦄ ⊢ ⓝU.T ¡[h, o] → ⦃G, L⦄ ⊢ ⓝU.T ¡[h, o, 0].
+#h #o #G #L #U #T #H elim (snv_inv_cast … H) -H
+#U0 #HU #HT #HU0 #HTU0 @shnv_cast // -HU -HT
+#d #H <(le_n_O_to_eq … H) -d /2 width=3 by scpds_div/
+qed.