lemma nta_inv_ldec_sn_cnv (h) (a) (G) (K) (V):
∀X2. ❪G,K.ⓛV❫ ⊢ #0 :[h,a] X2 →
- ∃∃U. ❪G,K❫ ⊢ V ![h,a] & ⇧*[1] V ≘ U & ❪G,K.ⓛV❫ ⊢ U ⬌*[h] X2 & ❪G,K.ⓛV❫ ⊢ X2 ![h,a].
+ ∃∃U. ❪G,K❫ ⊢ V ![h,a] & ⇧[1] V ≘ U & ❪G,K.ⓛV❫ ⊢ U ⬌*[h] X2 & ❪G,K.ⓛV❫ ⊢ X2 ![h,a].
#h #a #G #Y #X #X2 #H
elim (cnv_inv_cast … H) -H #X1 #HX2 #H1 #HX21 #H2
elim (cnv_inv_zero … H1) -H1 #Z #K #V #HV #H destruct