-fact aaa_ind_csx_alt_aux: ∀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⦄ ⊢ ⬊*[h, o] T → ⦃G, L⦄ ⊢ T ⁝ A → R T.
-#h #o #G #L #A #R #IH #T #H @(csx_ind_alt … H) -T /4 width=5 by cpxs_aaa_conf/
+fact aaa_ind_csx_cpxs_aux (G) (L):
+ ∀A. ∀Q:predicate ….
+ (∀T1. ❨G,L❩ ⊢ T1 ⁝ A →
+ (∀T2. ❨G,L❩ ⊢ T1 ⬈* T2 → (T1 ≅ T2 → ⊥) → Q T2) → Q T1
+ ) →
+ ∀T. ❨G,L❩ ⊢ ⬈*𝐒 T → ❨G,L❩ ⊢ T ⁝ A → Q T.
+#G #L #A #Q #IH #T #H @(csx_ind_cpxs … H) -T /4 width=5 by cpxs_aaa_conf/