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 13e746d7fc05bd8104ae62444dab0e551bb52a9d..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
@@ -12,70 +12,60 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/notation/relations/predtynormal_5.ma".
-include "static_2/syntax/tdeq.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. sd h → relation3 genv lenv term ≝
-                λh,o,G,L. NF … (cpx h G L) (tdeq h o …).
+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 o G L T = (cnx h o 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_sort: ∀h,o,G,L,s. ⦃G, L⦄ ⊢ ⬈[h, o] 𝐍⦃⋆s⦄ → deg h o s 0.
-#h #o #G #L #s #H
-lapply (H (⋆(next h s)) ?) -H /2 width=2 by cpx_ess/ -G -L #H
-elim (tdeq_inv_sort1 … H) -H #s0 #d #H1 #H2 #H destruct
-lapply (deg_next … H1) #H0
-lapply (deg_mono … H0 … H2) -H0 -H2 #H
-<(pred_inv_refl … H) -H //
-qed-.
-
-lemma cnx_inv_abst: ∀h,o,p,G,L,V,T. ⦃G, L⦄ ⊢ ⬈[h, o] 𝐍⦃ⓛ{p}V.T⦄ →
-                    ⦃G, L⦄ ⊢ ⬈[h, o] 𝐍⦃V⦄ ∧ ⦃G, L.ⓛV⦄ ⊢ ⬈[h, o] 𝐍⦃T⦄.
-#h #o #p #G #L #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
+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
 ]
-#H elim (tdeq_inv_pair … H) -H //
+#H elim (teqx_inv_pair … H) -H //
 qed-.
 
 (* Basic_2A1: was: cnx_inv_abbr *)
-lemma cnx_inv_abbr_neg: ∀h,o,G,L,V,T. ⦃G, L⦄ ⊢ ⬈[h, o] 𝐍⦃-ⓓV.T⦄ →
-                        ⦃G, L⦄ ⊢ ⬈[h, o] 𝐍⦃V⦄ ∧ ⦃G, L.ⓓV⦄ ⊢ ⬈[h, o] 𝐍⦃T⦄.
-#h #o #G #L #V1 #T1 #HVT1 @conj
-[ #V2 #HV2 lapply (HVT1 (-ⓓV2.T1) ?) -HVT1 /2 width=2 by cpx_pair_sn/ -HV2 
+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
 ]
-#H elim (tdeq_inv_pair … H) -H //
+#H elim (teqx_inv_pair … H) -H //
 qed-.
 
 (* Basic_2A1: was: cnx_inv_eps *)
-lemma cnx_inv_cast: ∀h,o,G,L,V,T. ⦃G, L⦄ ⊢ ⬈[h, o] 𝐍⦃ⓝV.T⦄ → ⊥.
-#h #o #G #L #V #T #H lapply (H T ?) -H
-/2 width=6 by cpx_eps, tdeq_inv_pair_xy_y/
+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,o,G,L,s. deg h o s 0 → ⦃G, L⦄ ⊢ ⬈[h, o] 𝐍⦃⋆s⦄.
-#h #o #G #L #s #Hs #X #H elim (cpx_inv_sort1 … H) -H
-/3 width=3 by tdeq_sort, deg_next/
-qed.
-
-lemma cnx_sort_iter: ∀h,o,G,L,s,d. deg h o s d → ⦃G, L⦄ ⊢ ⬈[h, o] 𝐍⦃⋆((next h)^d s)⦄.
-#h #o #G #L #s #d #Hs lapply (deg_iter … d Hs) -Hs
-<minus_n_n /2 width=6 by cnx_sort/
+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,o,p,G,L,W,T. ⦃G, L⦄ ⊢ ⬈[h, o] 𝐍⦃W⦄ → ⦃G, L.ⓛW⦄ ⊢ ⬈[h, o] 𝐍⦃T⦄ →
-                ⦃G, L⦄ ⊢ ⬈[h, o] 𝐍⦃ⓛ{p}W.T⦄.
-#h #o #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
-@tdeq_pair [ @HW | @HT ] // (**) (* auto fails because δ-expansion gets in the way *)
+@teqx_pair [ @HW | @HT ] // (**) (* auto fails because δ-expansion gets in the way *)
 qed.