update in basic_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/etc/nta/nta.etc b/matita/matita/contribs/lambdadelta/basic_2/etc/nta/nta.etc
index 7c9fc0d69df9b66bdf2b941365e8d404e1853db5..166fd2105a13bd98cf1938e2ccc1a2470d3f3912 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/etc/nta/nta.etc
+++ b/matita/matita/contribs/lambdadelta/basic_2/etc/nta/nta.etc
@@ -1,3 +1,7 @@
+(* Basic_1: was by definition: ty3_abst *)
+(* Basic_2A1: was by definition: nta_ldec ntaa_ldec *)
+lemma nta_ldec_drops
+
 (* Basic_1: was by definition: ty3_bind *)
 (* Basic_2A1: was by definition: nta_bind ntaa_bind *)
 lemma nta_bind
@@ -9,31 +13,51 @@ lemma nta_pure
 (* Basic_2A1: was: nta_inv_bind1 ntaa_inv_bind1 *)
 lemma nta_inv_bind_sn
 
-| ntaa_cast: ∀L,T,U,W. ntaa h L T U → ntaa h L U W → ntaa h L (ⓝU. T) U
+(* Basic_1: was: ty3_gen_lref *)
+(* Basic_2A1: was: nta_inv_lref1 *)
+lemma nta_inv_lref_sn_drops
+
+(* Basic_1: uses: ty3_gen_abst_abst *)
+lemma nta_inv_abst_bi
 
 (* Advanced properties ******************************************************)
 
+| ntaa_cast: ∀L,T,U,W. ntaa h L T U → ntaa h L U W → ntaa h L (ⓝU. T) U
+
 lemma nta_cast_alt: ∀h,L,T,W,U. ⦃h, L⦄ ⊢ T  : W → ⦃h, L⦄ ⊢ T : U → ⦃h, L⦄ ⊢ ⓝW.T : U.
 #h #L #T #W #U #HTW #HTU
 lapply (nta_mono … HTW … HTU) #HWU
 elim (nta_fwd_correct … HTU) -HTU /3 width=3/
 qed.
 
-lemma nta_inv_cast1: ∀h,L,X,Y,U. ⦃h, L⦄ ⊢ ⓝY.X : U →  ⦃h, L⦄ ⊢ X : Y ∧ L ⊢ Y ⬌* U.
-/2 width=3/ qed-.
-
-(* Basic_1: uses: ty3_gen_cast *)
-lemma nta_inv_cast_sn_old (a) (h) (G) (L) (X2):
-      ∀T0,T1. ⦃G,L⦄ ⊢ ⓝT1.T0 :[a,h] X2 →
-      ∃∃T2. ⦃G,L⦄ ⊢ T0 :[a,h] T1 & ⦃G,L⦄ ⊢ T1 :[a,h] T2 & ⦃G,L⦄ ⊢ ⓝT2.T1 ⬌*[h] X2 & ⦃G,L⦄ ⊢ X2 ![a,h].
-
-(* Basic_1: was: ty3_typecheck *)
-lemma nta_typecheck: ∀h,L,T,U. ⦃h, L⦄ ⊢ T : U → ∃T0. ⦃h, L⦄ ⊢ ⓝU.T : T0.
-/3 width=2/ qed.
-
-(* Basic_1: was: ty3_correct *)
-(* Basic_2A1: was: ntaa_fwd_correct *)
-lemma nta_fwd_correct: ∀h,L,T,U. ⦃h, L⦄ ⊢ T : U → ∃T0. ⦃h, L⦄ ⊢ U : T0.
-#h #L #T #U #H
-elim (ntaa_fwd_correct … (nta_ntaa … H)) -H /3 width=2 by ntaa_nta, ex_intro/
-qed-.
+lemma nta_ind_alt: ∀h. ∀Q:lenv→relation term.
+   (∀L,k. Q L ⋆k ⋆(next h k)) →
+   (∀L,K,V,W,U,i.
+      ⇩[O, i] L ≡ K.ⓓV → ⦃h, K⦄ ⊢ V : W → ⇧[O, i + 1] W ≡ U →
+      Q K V W → Q L (#i) U
+   ) →
+   (∀L,K,W,V,U,i.
+      ⇩[O, i] L ≡ K.ⓛW → ⦃h, K⦄ ⊢ W : V → ⇧[O, i + 1] W ≡ U →
+      Q K W V → Q L (#i) U
+   ) →
+   (∀I,L,V,W,T,U.
+      ⦃h, L⦄ ⊢ V : W → ⦃h, L.ⓑ{I}V⦄ ⊢ T : U →
+      Q L V W → Q (L.ⓑ{I}V) T U → Q L (ⓑ{I}V.T) (ⓑ{I}V.U)
+   ) →
+   (∀L,V,W,T,U.
+      ⦃h, L⦄ ⊢ V : W → ⦃h, L⦄ ⊢ (ⓛW.T):(ⓛW.U) →
+      Q L V W →Q L (ⓛW.T) (ⓛW.U) →Q L (ⓐV.ⓛW.T) (ⓐV.ⓛW.U)
+   ) →
+   (∀L,V,W,T,U.
+      ⦃h, L⦄ ⊢ T : U → ⦃h, L⦄ ⊢ (ⓐV.U) : W →
+      Q L T U → Q L (ⓐV.U) W → Q L (ⓐV.T) (ⓐV.U)
+   ) →
+   (∀L,T,U,W.
+      ⦃h, L⦄ ⊢ T : U → ⦃h, L⦄ ⊢ U : W →
+      Q L T U → Q L U W → Q L (ⓝU.T) U
+   ) →
+   (∀L,T,U1,U2,V2.
+      ⦃h, L⦄ ⊢ T : U1 → L ⊢ U1 ⬌* U2 → ⦃h, L⦄ ⊢ U2 : V2 →
+      Q L T U1 →Q L U2 V2 →Q L T U2
+   ) →
+   ∀L,T,U. ⦃h, L⦄ ⊢ T : U → Q L T U.