(* Properties on partial unfold on local environments ***********************)
-lemma delift_ltpss_conf_eq: ∀L,T1,T2,d,e. L ⊢ T1 [d, e] ≡ T2 →
- ∀K. L ▶* [d, e] K → K ⊢ T1 [d, e] ≡ T2.
+lemma delift_ltpss_conf_eq: ∀L,T1,T2,d,e. L ⊢ T1 ▼*[d, e] ≡ T2 →
+ ∀K. L ▶* [d, e] K → K ⊢ T1 ▼*[d, e] ≡ T2.
#L #T1 #T2 #d #e * #T #HT1 #HT2 #K #HLK
elim (ltpss_tpss_conf … HT1 … HLK) -L #T0 #HT10 #HT0
lapply (tpss_inv_lift1_eq … HT0 … HT2) -HT0 #H destruct /2 width=3/
qed.
lemma ltpss_delift_trans_eq: ∀L,K,d,e. L ▶* [d, e] K →
- ∀T1,T2. K ⊢ T1 [d, e] ≡ T2 → L ⊢ T1 [d, e] ≡ T2.
+ ∀T1,T2. K ⊢ T1 ▼*[d, e] ≡ T2 → L ⊢ T1 ▼*[d, e] ≡ T2.
#L #K #d #e #HLK #T1 #T2 * #T #HT1 #HT2
lapply (ltpss_tpss_trans_eq … HT1 … HLK) -K /2 width=3/
qed.