(* Note: probably this is an inversion lemma *)
(* Basic_2A1: was: cpxs_fwd_delta *)
lemma cpxs_fwd_delta_drops (h) (I) (G) (L) (K):
- ∀V1,i. ⇩*[i] L ≘ K.ⓑ[I]V1 →
- ∀V2. ⇧*[↑i] V1 ≘ V2 →
+ ∀V1,i. ⇩[i] L ≘ K.ⓑ[I]V1 →
+ ∀V2. ⇧[↑i] V1 ≘ V2 →
∀X2. ❪G,L❫ ⊢ #i ⬈*[h] X2 →
∨∨ #i ⩳ X2 | ❪G,L❫ ⊢ V2 ⬈*[h] X2.
#h #I #G #L #K #V1 #i #HLK #V2 #HV12 #X2 #H
lemma cpxs_fwd_theta (h) (p) (G) (L):
∀V1,V,T,X2. ❪G,L❫ ⊢ ⓐV1.ⓓ[p]V.T ⬈*[h] X2 →
- ∀V2. ⇧*[1] V1 ≘ V2 →
+ ∀V2. ⇧[1] V1 ≘ V2 →
∨∨ ⓐV1.ⓓ[p]V.T ⩳ X2 | ❪G,L❫ ⊢ ⓓ[p]V.ⓐV2.T ⬈*[h] X2.
#h #p #G #L #V1 #V #T #X2 #H #V2 #HV12
elim (cpxs_inv_appl1 … H) -H *