-lemma lprs_ind_dx: ∀L2. ∀R:predicate lenv. R L2 →
- (∀L1,L. L1 ⊢ ➡ L → L ⊢ ➡* L2 → R L → R L1) →
- ∀L1. L1 ⊢ ➡* L2 → R L1.
-#L2 #R #HL2 #IHL2 #L1 #HL12
+lemma lprs_ind_dx: ∀G,L2. ∀R:predicate lenv. R L2 →
+ (∀L1,L. ⦃G, L1⦄ ⊢ ➡ L → ⦃G, L⦄ ⊢ ➡* L2 → R L → R L1) →
+ ∀L1. ⦃G, L1⦄ ⊢ ➡* L2 → R L1.
+#G #L2 #R #HL2 #IHL2 #L1 #HL12