(* Basic inversion lemmas ***************************************************)
lemma cnr_inv_abst (h) (p) (G) (L):
- â\88\80V,T. â\9dªG,Lâ\9d« ⊢ ➡𝐍[h,0] ⓛ[p]V.T →
- â\88§â\88§ â\9dªG,Lâ\9d« â\8a¢ â\9e¡ð\9d\90\8d[h,0] V & â\9dªG,L.â\93\9bVâ\9d« ⊢ ➡𝐍[h,0] T.
+ â\88\80V,T. â\9d¨G,Lâ\9d© ⊢ ➡𝐍[h,0] ⓛ[p]V.T →
+ â\88§â\88§ â\9d¨G,Lâ\9d© â\8a¢ â\9e¡ð\9d\90\8d[h,0] V & â\9d¨G,L.â\93\9bVâ\9d© ⊢ ➡𝐍[h,0] T.
#h #p #G #L #V1 #T1 #HVT1 @conj
[ #V2 #HV2 lapply (HVT1 (ⓛ[p]V2.T1) ?) -HVT1 /2 width=2 by cpr_pair_sn/ -HV2 #H destruct //
| #T2 #HT2 lapply (HVT1 (ⓛ[p]V1.T2) ?) -HVT1 /2 width=2 by cpm_bind/ -HT2 #H destruct //
(* Basic_2A1: was: cnr_inv_abbr *)
lemma cnr_inv_abbr_neg (h) (G) (L):
- â\88\80V,T. â\9dªG,Lâ\9d« ⊢ ➡𝐍[h,0] -ⓓV.T →
- â\88§â\88§ â\9dªG,Lâ\9d« â\8a¢ â\9e¡ð\9d\90\8d[h,0] V & â\9dªG,L.â\93\93Vâ\9d« ⊢ ➡𝐍[h,0] T.
+ â\88\80V,T. â\9d¨G,Lâ\9d© ⊢ ➡𝐍[h,0] -ⓓV.T →
+ â\88§â\88§ â\9d¨G,Lâ\9d© â\8a¢ â\9e¡ð\9d\90\8d[h,0] V & â\9d¨G,L.â\93\93Vâ\9d© ⊢ ➡𝐍[h,0] T.
#h #G #L #V1 #T1 #HVT1 @conj
[ #V2 #HV2 lapply (HVT1 (-ⓓV2.T1) ?) -HVT1 /2 width=2 by cpr_pair_sn/ -HV2 #H destruct //
| #T2 #HT2 lapply (HVT1 (-ⓓV1.T2) ?) -HVT1 /2 width=2 by cpm_bind/ -HT2 #H destruct //
(* Basic_2A1: was: cnr_inv_eps *)
lemma cnr_inv_cast (h) (G) (L):
- â\88\80V,T. â\9dªG,Lâ\9d« ⊢ ➡𝐍[h,0] ⓝV.T → ⊥.
+ â\88\80V,T. â\9d¨G,Lâ\9d© ⊢ ➡𝐍[h,0] ⓝV.T → ⊥.
#h #G #L #V #T #H lapply (H T ?) -H
/2 width=4 by cpm_eps, discr_tpair_xy_y/
qed-.
(* Basic_1: was: nf2_sort *)
lemma cnr_sort (h) (G) (L):
- â\88\80s. â\9dªG,Lâ\9d« ⊢ ➡𝐍[h,0] ⋆s.
+ â\88\80s. â\9d¨G,Lâ\9d© ⊢ ➡𝐍[h,0] ⋆s.
#h #G #L #s #X #H
>(cpr_inv_sort1 … H) //
qed.
lemma cnr_gref (h) (G) (L):
- â\88\80l. â\9dªG,Lâ\9d« ⊢ ➡𝐍[h,0] §l.
+ â\88\80l. â\9d¨G,Lâ\9d© ⊢ ➡𝐍[h,0] §l.
#h #G #L #l #X #H
>(cpr_inv_gref1 … H) //
qed.
(* Basic_1: was: nf2_abst *)
lemma cnr_abst (h) (p) (G) (L):
- â\88\80W,T. â\9dªG,Lâ\9d« â\8a¢ â\9e¡ð\9d\90\8d[h,0] W â\86\92 â\9dªG,L.â\93\9bWâ\9d« â\8a¢ â\9e¡ð\9d\90\8d[h,0] T â\86\92 â\9dªG,Lâ\9d« ⊢ ➡𝐍[h,0] ⓛ[p]W.T.
+ â\88\80W,T. â\9d¨G,Lâ\9d© â\8a¢ â\9e¡ð\9d\90\8d[h,0] W â\86\92 â\9d¨G,L.â\93\9bWâ\9d© â\8a¢ â\9e¡ð\9d\90\8d[h,0] T â\86\92 â\9d¨G,Lâ\9d© ⊢ ➡𝐍[h,0] ⓛ[p]W.T.
#h #p #G #L #W #T #HW #HT #X #H
elim (cpm_inv_abst1 … H) -H #W0 #T0 #HW0 #HT0 #H destruct
<(HW … HW0) -W0 <(HT … HT0) -T0 //
qed.
lemma cnr_abbr_neg (h) (G) (L):
- â\88\80V,T. â\9dªG,Lâ\9d« â\8a¢ â\9e¡ð\9d\90\8d[h,0] V â\86\92 â\9dªG,L.â\93\93Vâ\9d« â\8a¢ â\9e¡ð\9d\90\8d[h,0] T â\86\92 â\9dªG,Lâ\9d« ⊢ ➡𝐍[h,0] -ⓓV.T.
+ â\88\80V,T. â\9d¨G,Lâ\9d© â\8a¢ â\9e¡ð\9d\90\8d[h,0] V â\86\92 â\9d¨G,L.â\93\93Vâ\9d© â\8a¢ â\9e¡ð\9d\90\8d[h,0] T â\86\92 â\9d¨G,Lâ\9d© ⊢ ➡𝐍[h,0] -ⓓV.T.
#h #G #L #V #T #HV #HT #X #H
elim (cpm_inv_abbr1 … H) -H *
[ #V0 #T0 #HV0 #HT0 #H destruct