update in basic_2 and ground_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/shnv.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/shnv.ma
index deacf88dd30813ef4abac72a851b969299e600fc..9616434185c6ddf5e0b921ac22e376184d66016b 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/shnv.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/shnv.ma
@@ -18,38 +18,38 @@ include "basic_2/dynamic/snv.ma".
 
 (* STRATIFIED HIGHER NATIVE VALIDITY FOR TERMS ******************************)
 
-inductive shnv (h) (g) (d1) (G) (L): predicate term ≝
-| shnv_cast: ∀U,T. ⦃G, L⦄ ⊢ U ¡[h, g] → ⦃G, L⦄ ⊢ T ¡[h, g] →
-             (∀d2. d2 ≤ d1 → ⦃G, L⦄ ⊢ U •*⬌*[h, g, d2, d2+1] T) →
-             shnv h g d1 G L (ⓝU.T)
+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 g d G L T = (shnv h g d G L T).
+   'NativeValid h o d G L T = (shnv h o d G L T).
 
 (* Basic inversion lemmas ***************************************************)
 
-fact shnv_inv_cast_aux: ∀h,g,G,L,X,d1. ⦃G, L⦄ ⊢ X ¡[h, g, d1] → ∀U,T. X = ⓝU.T →
-                        ∧∧ ⦃G, L⦄ ⊢ U ¡[h, g] & ⦃G, L⦄ ⊢ T ¡[h, g]
-                         & (∀d2. d2 ≤ d1 → ⦃G, L⦄ ⊢ U •*⬌*[h, g, d2, d2+1] T).
-#h #g #G #L #X #d1 * -X
+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,g,G,L,U,T,d1. ⦃G, L⦄ ⊢ ⓝU.T ¡[h, g, d1] →
-                     ∧∧ ⦃G, L⦄ ⊢ U ¡[h, g] & ⦃G, L⦄ ⊢ T ¡[h, g]
-                      & (∀d2. d2 ≤ d1 → ⦃G, L⦄ ⊢ U •*⬌*[h, g, d2, d2+1] T).
+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,g,G,L,T,d. ⦃G, L⦄ ⊢ T ¡[h, g, d] → ⦃G, L⦄ ⊢ T ¡[h, g].
-#h #g #G #L #T #d * -T
+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,g,G,L,U,T. ⦃G, L⦄ ⊢ ⓝU.T ¡[h, g] → ⦃G, L⦄ ⊢ ⓝU.T ¡[h, g, 0].
-#h #g #G #L #U #T #H elim (snv_inv_cast … H) -H
+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.