(* Properties concerning context-sensitive parallel reduction on lenv's *****)
-lemma ltpr_tpss_trans: ∀L1,L2. L1 ➡ L2 → ∀T1,T2,d,e. L2 ⊢ T1 [d, e] ▶* T2 →
- ∃∃T. L1 ⊢ T1 [d, e] ▶* T & L1 ⊢ T ➡* T2.
+lemma ltpr_tpss_trans: ∀L1,L2. L1 ➡ L2 → ∀T1,T2,d,e. L2 ⊢ T1 ▶* [d, e] T2 →
+ ∃∃T. L1 ⊢ T1 ▶* [d, e] T & L1 ⊢ T ➡* T2.
#L1 #L2 #HL12 #T1 #T2 #d #e #H @(tpss_ind … H) -T2
[ /2 width=3/
| #T #T2 #_ #HT2 * #T0 #HT10 #HT0