milestone update in basic_2, update in ground and static_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / rt_transition / cnx.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cnx.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cnx.ma
index 1aa7d1daa1a911daf45736be8b9db58f501e318f..f958591d49b12ee31cf5e980a6903a31c1a8d757 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cnx.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cnx.ma
@@ -12,24 +12,25 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/notation/relations/predtynormal_4.ma".
+include "basic_2/notation/relations/predtynormal_3.ma".
 include "static_2/syntax/teqx.ma".
 include "basic_2/rt_transition/cpx.ma".
 
-(* NORMAL TERMS FOR UNBOUND CONTEXT-SENSITIVE PARALLEL RT-TRANSITION ********)
+(* NORMAL TERMS FOR EXTENDED CONTEXT-SENSITIVE PARALLEL RT-TRANSITION *******)
 
-definition cnx: ∀h. relation3 genv lenv term ≝
-                λh,G,L. NF … (cpx h G L) teqx.
+definition cnx: relation3 genv lenv term ≝
+           λG,L. NF … (cpx G L) teqx.
 
 interpretation
-   "normality for unbound context-sensitive parallel rt-transition (term)"
-   'PRedTyNormal h G L T = (cnx h G L T).
+  "normality for extended context-sensitive parallel rt-transition (term)"
+  'PRedTyNormal G L T = (cnx G L T).
 
 (* Basic inversion lemmas ***************************************************)
 
-lemma cnx_inv_abst: ∀h,p,G,L,V,T. ❪G,L❫ ⊢ ⬈𝐍[h] ⓛ[p]V.T →
-                    ∧∧ ❪G,L❫ ⊢ ⬈𝐍[h] V & ❪G,L.ⓛV❫ ⊢ ⬈𝐍[h] T.
-#h #p #G #L #V1 #T1 #HVT1 @conj
+lemma cnx_inv_abst (G) (L):
+      ∀p,V,T. ❪G,L❫ ⊢ ⬈𝐍 ⓛ[p]V.T →
+      ∧∧ ❪G,L❫ ⊢ ⬈𝐍 V & ❪G,L.ⓛV❫ ⊢ ⬈𝐍 T.
+#G #L #p #V1 #T1 #HVT1 @conj
 [ #V2 #HV2 lapply (HVT1 (ⓛ[p]V2.T1) ?) -HVT1 /2 width=2 by cpx_pair_sn/ -HV2
 | #T2 #HT2 lapply (HVT1 (ⓛ[p]V1.T2) ?) -HVT1 /2 width=2 by cpx_bind/ -HT2
 ]
@@ -37,9 +38,10 @@ lemma cnx_inv_abst: ∀h,p,G,L,V,T. ❪G,L❫ ⊢ ⬈𝐍[h] ⓛ[p]V.T →
 qed-.
 
 (* Basic_2A1: was: cnx_inv_abbr *)
-lemma cnx_inv_abbr_neg: ∀h,G,L,V,T. ❪G,L❫ ⊢ ⬈𝐍[h] -ⓓV.T →
-                        ∧∧ ❪G,L❫ ⊢ ⬈𝐍[h] V & ❪G,L.ⓓV❫ ⊢ ⬈𝐍[h] T.
-#h #G #L #V1 #T1 #HVT1 @conj
+lemma cnx_inv_abbr_neg (G) (L):
+      ∀V,T. ❪G,L❫ ⊢ ⬈𝐍 -ⓓV.T →
+      ∧∧ ❪G,L❫ ⊢ ⬈𝐍 V & ❪G,L.ⓓV❫ ⊢ ⬈𝐍 T.
+#G #L #V1 #T1 #HVT1 @conj
 [ #V2 #HV2 lapply (HVT1 (-ⓓV2.T1) ?) -HVT1 /2 width=2 by cpx_pair_sn/ -HV2
 | #T2 #HT2 lapply (HVT1 (-ⓓV1.T2) ?) -HVT1 /2 width=2 by cpx_bind/ -HT2
 ]
@@ -47,21 +49,23 @@ lemma cnx_inv_abbr_neg: ∀h,G,L,V,T. ❪G,L❫ ⊢ ⬈𝐍[h] -ⓓV.T →
 qed-.
 
 (* Basic_2A1: was: cnx_inv_eps *)
-lemma cnx_inv_cast: ∀h,G,L,V,T. ❪G,L❫ ⊢ ⬈𝐍[h] ⓝV.T → ⊥.
-#h #G #L #V #T #H lapply (H T ?) -H
+lemma cnx_inv_cast (G) (L):
+      ∀V,T. ❪G,L❫ ⊢ ⬈𝐍 ⓝV.T → ⊥.
+#G #L #V #T #H lapply (H T ?) -H
 /2 width=6 by cpx_eps, teqx_inv_pair_xy_y/
 qed-.
 
 (* Basic properties *********************************************************)
 
-lemma cnx_sort: ∀h,G,L,s. ❪G,L❫ ⊢ ⬈𝐍[h] ⋆s.
-#h #G #L #s #X #H elim (cpx_inv_sort1 … H) -H
+lemma cnx_sort (G) (L):
+      ∀s. ❪G,L❫ ⊢ ⬈𝐍 ⋆s.
+#G #L #s #X #H elim (cpx_inv_sort1 … H) -H
 /2 width=1 by teqx_sort/
 qed.
 
-lemma cnx_abst: ∀h,p,G,L,W,T. ❪G,L❫ ⊢ ⬈𝐍[h] W → ❪G,L.ⓛW❫ ⊢ ⬈𝐍[h] T →
-                ❪G,L❫ ⊢ ⬈𝐍[h] ⓛ[p]W.T.
-#h #p #G #L #W #T #HW #HT #X #H
+lemma cnx_abst (G) (L):
+      ∀p,W,T. ❪G,L❫ ⊢ ⬈𝐍 W → ❪G,L.ⓛW❫ ⊢ ⬈𝐍 T → ❪G,L❫ ⊢ ⬈𝐍 ⓛ[p]W.T.
+#G #L #p #W #T #HW #HT #X #H
 elim (cpx_inv_abst1 … H) -H #W0 #T0 #HW0 #HT0 #H destruct
 @teqx_pair [ @HW | @HT ] // (**) (* auto fails because δ-expansion gets in the way *)
 qed.