-fact aaa_ind_csx_cpxs_aux: ∀h,G,L,A. ∀Q:predicate term.
- (∀T1. ❪G,L❫ ⊢ T1 ⁝ A →
- (∀T2. ❪G,L❫ ⊢ T1 ⬈*[h] T2 → (T1 ≛ T2 → ⊥) → Q T2) → Q T1
- ) →
- ∀T. ❪G,L❫ ⊢ ⬈*[h] 𝐒❪T❫ → ❪G,L❫ ⊢ T ⁝ A → Q T.
-#h #G #L #A #Q #IH #T #H @(csx_ind_cpxs … 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/