(* 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⦄ ⊢ ➡[h] 𝐍⦃ⓐV.T⦄ → ∧∧ ⦃G,L⦄ ⊢ ➡[h] 𝐍⦃V⦄ & ⦃G,L⦄ ⊢ ➡[h] 𝐍⦃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⦄ ⊢ ➡[h] 𝐍⦃V⦄ → ⦃G,L⦄ ⊢ ➡[h] 𝐍⦃T⦄ → 𝐒⦃T⦄ → ⦃G,L⦄ ⊢ ➡[h] 𝐍⦃ⓐ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 //