(* Inversion lemmas with simple terms ***************************************)
lemma cnr_inv_appl (h) (G) (L):
- ∀V,T. ❪G,L❫ ⊢ ➡[h] 𝐍❪ⓐV.T❫ → ∧∧ ❪G,L❫ ⊢ ➡[h] 𝐍❪V❫ & ❪G,L❫ ⊢ ➡[h] 𝐍❪T❫ & 𝐒❪T❫.
+ ∀V,T. ❪G,L❫ ⊢ ➡𝐍[h,0] ⓐV.T →
+ ∧∧ ❪G,L❫ ⊢ ➡𝐍[h,0] V & ❪G,L❫ ⊢ ➡𝐍[h,0] T & 𝐒❪T❫.
#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):
- ∀V,T. ❪G,L❫ ⊢ ➡[h] 𝐍❪V❫ → ❪G,L❫ ⊢ ➡[h] 𝐍❪T❫ → 𝐒❪T❫ → ❪G,L❫ ⊢ ➡[h] 𝐍❪ⓐV.T❫.
+ ∀V,T. ❪G,L❫ ⊢ ➡𝐍[h,0] V → ❪G,L❫ ⊢ ➡𝐍[h,0] T → 𝐒❪T❫ → ❪G,L❫ ⊢ ➡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 //