-lemma cpxs_ind_dx: ∀h,G,L,T2. ∀R:predicate term. R T2 →
- (∀T1,T. ⦃G, L⦄ ⊢ T1 ⬈[h] T → ⦃G, L⦄ ⊢ T ⬈*[h] T2 → R T → R T1) →
- ∀T1. ⦃G, L⦄ ⊢ T1 ⬈*[h] T2 → R T1.
-#h #G #L #T2 #R #HT2 #IHT2 #T1 #HT12
+lemma cpxs_ind_dx: ∀h,G,L,T2. ∀Q:predicate term. Q T2 →
+ (∀T1,T. ⦃G, L⦄ ⊢ T1 ⬈[h] T → ⦃G, L⦄ ⊢ T ⬈*[h] T2 → Q T → Q T1) →
+ ∀T1. ⦃G, L⦄ ⊢ T1 ⬈*[h] T2 → Q T1.
+#h #G #L #T2 #Q #HT2 #IHT2 #T1 #HT12