(* Inversion lemmas with simple terms ***************************************)
lemma cnr_inv_appl (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,Lâ\9d« â\8a¢ â\9e¡ð\9d\90\8d[h,0] T & ð\9d\90\92â\9dªTâ\9d«.
+ 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,Lâ\9d© â\8a¢ â\9e¡ð\9d\90\8d[h,0] T & ð\9d\90\92â\9d¨Tâ\9d©.
#h #G #L #V1 #T1 #HVT1 @and3_intro
[ #V2 #HV2 lapply (HVT1 (ⓐV2.T1) ?) -HVT1 /2 width=1 by cpr_pair_sn/ -HV2 #H destruct //
| #T2 #HT2 lapply (HVT1 (ⓐV1.T2) ?) -HVT1 /2 width=1 by cpr_flat/ -HT2 #H destruct //
(* Basic_1: was only: nf2_appl_lref *)
lemma cnr_appl_simple (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,Lâ\9d« â\8a¢ â\9e¡ð\9d\90\8d[h,0] T â\86\92 ð\9d\90\92â\9dªTâ\9d« 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,Lâ\9d© â\8a¢ â\9e¡ð\9d\90\8d[h,0] T â\86\92 ð\9d\90\92â\9d¨Tâ\9d© â\86\92 â\9d¨G,Lâ\9d© ⊢ ➡𝐍[h,0] ⓐV.T.
#h #G #L #V #T #HV #HT #HS #X #H
elim (cpm_inv_appl1_simple … H) -H // #V0 #T0 #HV0 #HT0 #H destruct
<(HV … HV0) -V0 <(HT … HT0) -T0 //