-lemma aaa_ind_csx_alt: ∀h,o,G,L,A. ∀R:predicate term.
- (∀T1. ⦃G, L⦄ ⊢ T1 ⁝ A →
- (∀T2. ⦃G, L⦄ ⊢ T1 ➡*[h, o] T2 → (T1 = T2 → ⊥) → R T2) → R T1
- ) →
- ∀T. ⦃G, L⦄ ⊢ T ⁝ A → R T.
-/5 width=9 by aaa_ind_csx_alt_aux, aaa_csx/ qed-.
+(* Basic_2A1: was: aaa_ind_csx_alt *)
+lemma aaa_ind_csx_cpxs: ∀h,o,G,L,A. ∀Q:predicate term.
+ (∀T1. ⦃G, L⦄ ⊢ T1 ⁝ A →
+ (∀T2. ⦃G, L⦄ ⊢ T1 ⬈*[h] T2 → (T1 ≛[h, o] T2 → ⊥) → Q T2) → Q T1
+ ) →
+ ∀T. ⦃G, L⦄ ⊢ T ⁝ A → Q T.
+/5 width=9 by aaa_ind_csx_cpxs_aux, aaa_csx/ qed-.