X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Frt_transition%2Fcnx.ma;h=4b9059643cf1676c9f0b83e38db9581a3b684821;hb=bd53c4e895203eb049e75434f638f26b5a161a2b;hp=cc2397d0f8dbf569165da561cac9bd99fc340cb1;hpb=fb4c641d43be3d601104751363782553bea0fb6b;p=helm.git

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 cc2397d0f..4b9059643 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cnx.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cnx.ma
@@ -12,70 +12,56 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/notation/relations/predtynormal_5.ma".
-include "static_2/syntax/tdeq.ma".
+include "basic_2/notation/relations/predtynormal_4.ma".
+include "static_2/syntax/teqx.ma".
 include "basic_2/rt_transition/cpx.ma".
 
 (* NORMAL TERMS FOR UNBOUND 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: ∀h. relation3 genv lenv term ≝
+                λh,G,L. NF … (cpx h 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).
+   'PRedTyNormal h G L T = (cnx h 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_fix_sn … 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: ∀h,p,G,L,V,T. ❪G,L❫ ⊢ ⬈[h] 𝐍❪ⓛ[p]V.T❫ →
+                    ❪G,L❫ ⊢ ⬈[h] 𝐍❪V❫ ∧ ❪G,L.ⓛV❫ ⊢ ⬈[h] 𝐍❪T❫.
+#h #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
 ]
-#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: ∀h,G,L,V,T. ❪G,L❫ ⊢ ⬈[h] 𝐍❪-ⓓV.T❫ →
+                        ❪G,L❫ ⊢ ⬈[h] 𝐍❪V❫ ∧ ❪G,L.ⓓV❫ ⊢ ⬈[h] 𝐍❪T❫.
+#h #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: ∀h,G,L,V,T. ❪G,L❫ ⊢ ⬈[h] 𝐍❪ⓝV.T❫ → ⊥.
+#h #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: ∀h,G,L,s. ❪G,L❫ ⊢ ⬈[h] 𝐍❪⋆s❫.
+#h #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: ∀h,p,G,L,W,T. ❪G,L❫ ⊢ ⬈[h] 𝐍❪W❫ → ❪G,L.ⓛW❫ ⊢ ⬈[h] 𝐍❪T❫ →
+                ❪G,L❫ ⊢ ⬈[h] 𝐍❪ⓛ[p]W.T❫.
+#h #p #G #L #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.