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