lemma delift_refl_O2: ∀L,T,d. L ⊢ ▼*[d, 0] T ≡ T.
/2 width=3/ qed.
-lemma delift_lsubs_trans: ∀L1,T1,T2,d,e. L1 ⊢ ▼*[d, e] T1 ≡ T2 →
+lemma delift_lsubr_trans: ∀L1,T1,T2,d,e. L1 ⊢ ▼*[d, e] T1 ≡ T2 →
∀L2. L2 ≼ [d, e] L1 → L2 ⊢ ▼*[d, e] T1 ≡ T2.
#L1 #T1 #T2 #d #e * /3 width=3/
qed.
L ⊢ ▼*[d, e] V1 ≡ V2 → L. ⓑ{I} V2 ⊢ ▼*[d+1, e] T1 ≡ T2 →
L ⊢ ▼*[d, e] ⓑ{a,I} V1. T1 ≡ ⓑ{a,I} V2. T2.
#a #I #L #V1 #V2 #T1 #T2 #d #e * #V #HV1 #HV2 * #T #HT1 #HT2
-lapply (tpss_lsubs_trans … HT1 (L. ⓑ{I} V) ?) -HT1 /2 width=1/ /3 width=5/
+lapply (tpss_lsubr_trans … HT1 (L. ⓑ{I} V) ?) -HT1 /2 width=1/ /3 width=5/
qed.
lemma delift_flat: ∀I,L,V1,V2,T1,T2,d,e.
#a #I #L #V1 #T1 #U2 #d #e * #U #HU #HU2
elim (tpss_inv_bind1 … HU) -HU #V #T #HV1 #HT1 #X destruct
elim (lift_inv_bind2 … HU2) -HU2 #V2 #T2 #HV2 #HT2
-lapply (tpss_lsubs_trans … HT1 (L. ⓑ{I} V2) ?) -HT1 /2 width=1/ /3 width=5/
+lapply (tpss_lsubr_trans … HT1 (L. ⓑ{I} V2) ?) -HT1 /2 width=1/ /3 width=5/
qed-.
lemma delift_inv_flat1: ∀I,L,V1,T1,U2,d,e. L ⊢ ▼*[d, e] ⓕ{I} V1. T1 ≡ U2 →