lemma delift_refl_O2: ∀L,T,d. L ⊢ T ▼*[d, 0] ≡ T.
/2 width=3/ qed.
-lemma delift_lsubs_conf: ∀L1,T1,T2,d,e. L1 ⊢ T1 ▼*[d, e] ≡ T2 →
- ∀L2. L1 ≼ [d, e] L2 → L2 ⊢ T1 ▼*[d, e] ≡ T2.
+lemma delift_lsubs_trans: ∀L1,T1,T2,d,e. L1 ⊢ T1 ▼*[d, e] ≡ T2 →
+ ∀L2. L2 ≼ [d, e] L1 → L2 ⊢ T1 ▼*[d, e] ≡ T2.
#L1 #T1 #T2 #d #e * /3 width=3/
qed.
L ⊢ V1 ▼*[d, e] ≡ V2 → L. ⓑ{I} V2 ⊢ T1 ▼*[d+1, e] ≡ T2 →
L ⊢ ⓑ{I} V1. T1 ▼*[d, e] ≡ ⓑ{I} V2. T2.
#I #L #V1 #V2 #T1 #T2 #d #e * #V #HV1 #HV2 * #T #HT1 #HT2
-lapply (tpss_lsubs_conf … HT1 (L. ⓑ{I} V) ?) -HT1 /2 width=1/ /3 width=5/
+lapply (tpss_lsubs_trans … HT1 (L. ⓑ{I} V) ?) -HT1 /2 width=1/ /3 width=5/
qed.
lemma delift_flat: ∀I,L,V1,V2,T1,T2,d,e.
#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_conf … HT1 (L. ⓑ{I} V2) ?) -HT1 /2 width=1/ /3 width=5/
+lapply (tpss_lsubs_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 ⊢ ⓕ{I} V1. T1 ▼*[d, e] ≡ U2 →