L ⊢ T1 ▶ [d, e] T → L ⊢ T ▶* [d, e] T2 → L ⊢ T1 ▶* [d, e] T2.
/2 width=3/ qed.
-lemma tpss_lsubs_trans: ∀L1,T1,T2,d,e. L1 ⊢ T1 ▶* [d, e] T2 →
+lemma tpss_lsubr_trans: ∀L1,T1,T2,d,e. L1 ⊢ T1 ▶* [d, e] T2 →
∀L2. L2 ≼ [d, e] L1 → L2 ⊢ T1 ▶* [d, e] T2.
/3 width=3/ qed.
| #T #T2 #_ #HT2 #IHT @step /2 width=5/ (**) (* /3 width=5/ is too slow *)
]
| #V #V2 #_ #HV12 #IHV #a #I #T1 #T2 #HT12
- lapply (tpss_lsubs_trans … HT12 (L. ⓑ{I} V) ?) -HT12 /2 width=1/ #HT12
+ lapply (tpss_lsubr_trans … HT12 (L. ⓑ{I} V) ?) -HT12 /2 width=1/ #HT12
lapply (IHV a … HT12) -IHV -HT12 #HT12 @step /2 width=5/ (**) (* /3 width=5/ is too slow *)
]
qed.
[ /2 width=5/
| #U #U2 #_ #HU2 * #V #T #HV1 #HT1 #H destruct
elim (tps_inv_bind1 … HU2) -HU2 #V2 #T2 #HV2 #HT2 #H
- 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-.