qed.
lemma csx_applv_delta_drops (h) (G):
- ∀I,L,K,V1,i. ⇩*[i] L ≘ K.ⓑ[I]V1 →
- ∀V2. ⇧*[↑i] V1 ≘ V2 →
+ ∀I,L,K,V1,i. ⇩[i] L ≘ K.ⓑ[I]V1 →
+ ∀V2. ⇧[↑i] V1 ≘ V2 →
∀Vs. ❪G,L❫ ⊢ ⬈*[h] 𝐒❪ⒶVs.V2❫ → ❪G,L❫ ⊢ ⬈*[h] 𝐒❪ⒶVs.#i❫.
#h #G #I #L #K #V1 #i #HLK #V2 #HV12 #Vs elim Vs -Vs
[ /4 width=11 by csx_inv_lifts, csx_lref_pair_drops, drops_isuni_fwd_drop2/
(* Basic_1: was just: sn3_appls_abbr *)
lemma csx_applv_theta (h) (G):
- ∀p,L,V1b,V2b. ⇧*[1] V1b ≘ V2b →
+ ∀p,L,V1b,V2b. ⇧[1] V1b ≘ V2b →
∀V,T. ❪G,L❫ ⊢ ⬈*[h] 𝐒❪ⓓ[p]V.ⒶV2b.T❫ → ❪G,L❫ ⊢ ⬈*[h] 𝐒❪ⒶV1b.ⓓ[p]V.T❫.
#h #G #p #L #V1b #V2b * -V1b -V2b /2 width=1 by/
#V1b #V2b #V1 #V2 #HV12 #H