update in basic_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 4b9059643cf1676c9f0b83e38db9581a3b684821..1aa7d1daa1a911daf45736be8b9db58f501e318f 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cnx.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cnx.ma
@@ -27,8 +27,8 @@ interpretation
 
 (* Basic inversion lemmas ***************************************************)
 
-lemma cnx_inv_abst: ∀h,p,G,L,V,T. ❪G,L❫ ⊢ ⬈[h] 𝐍❪ⓛ[p]V.T❫ →
-                    â\9dªG,Lâ\9d« â\8a¢ â¬\88[h] ð\9d\90\8dâ\9dªVâ\9d« â\88§ â\9dªG,L.â\93\9bVâ\9d« â\8a¢ â¬\88[h] ð\9d\90\8dâ\9dªTâ\9d«.
+lemma cnx_inv_abst: ∀h,p,G,L,V,T. ❪G,L❫ ⊢ ⬈𝐍[h] ⓛ[p]V.T →
+                    â\88§â\88§ â\9dªG,Lâ\9d« â\8a¢ â¬\88ð\9d\90\8d[h] V & â\9dªG,L.â\93\9bVâ\9d« â\8a¢ â¬\88ð\9d\90\8d[h] 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
@@ -37,8 +37,8 @@ lemma cnx_inv_abst: ∀h,p,G,L,V,T. ❪G,L❫ ⊢ ⬈[h] 𝐍❪ⓛ[p]V.T❫ →
 qed-.
 
 (* Basic_2A1: was: cnx_inv_abbr *)
-lemma cnx_inv_abbr_neg: ∀h,G,L,V,T. ❪G,L❫ ⊢ ⬈[h] 𝐍❪-ⓓV.T❫ →
-                        â\9dªG,Lâ\9d« â\8a¢ â¬\88[h] ð\9d\90\8dâ\9dªVâ\9d« â\88§ â\9dªG,L.â\93\93Vâ\9d« â\8a¢ â¬\88[h] ð\9d\90\8dâ\9dªTâ\9d«.
+lemma cnx_inv_abbr_neg: ∀h,G,L,V,T. ❪G,L❫ ⊢ ⬈𝐍[h] -ⓓV.T →
+                        â\88§â\88§ â\9dªG,Lâ\9d« â\8a¢ â¬\88ð\9d\90\8d[h] V & â\9dªG,L.â\93\93Vâ\9d« â\8a¢ â¬\88ð\9d\90\8d[h] 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
@@ -47,20 +47,20 @@ lemma cnx_inv_abbr_neg: ∀h,G,L,V,T. ❪G,L❫ ⊢ ⬈[h] 𝐍❪-ⓓV.T❫ →
 qed-.
 
 (* Basic_2A1: was: cnx_inv_eps *)
-lemma cnx_inv_cast: ∀h,G,L,V,T. ❪G,L❫ ⊢ ⬈[h] 𝐍❪ⓝV.T❫ → ⊥.
+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
 /2 width=6 by cpx_eps, teqx_inv_pair_xy_y/
 qed-.
 
 (* Basic properties *********************************************************)
 
-lemma cnx_sort: ∀h,G,L,s. ❪G,L❫ ⊢ ⬈[h] 𝐍❪⋆s❫.
+lemma cnx_sort: ∀h,G,L,s. ❪G,L❫ ⊢ ⬈𝐍[h] ⋆s.
 #h #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❫ ⊢ ⬈[h] 𝐍❪W❫ → ❪G,L.ⓛW❫ ⊢ ⬈[h] 𝐍❪T❫ →
-                ❪G,L❫ ⊢ ⬈[h] 𝐍❪ⓛ[p]W.T❫.
+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
 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 *)