(* Main properties with atomic arity assignment *****************************)
-theorem aaa_csx: â\88\80h,G,L,T,A. â¦\83G,Lâ¦\84 â\8a¢ T â\81\9d A â\86\92 â¦\83G,Lâ¦\84 â\8a¢ â¬\88*[h] ð\9d\90\92â¦\83Tâ¦\84.
+theorem aaa_csx: â\88\80h,G,L,T,A. â\9dªG,Lâ\9d« â\8a¢ T â\81\9d A â\86\92 â\9dªG,Lâ\9d« â\8a¢ â¬\88*[h] ð\9d\90\92â\9dªTâ\9d«.
#h #G #L #T #A #H
@(gcr_aaa … (csx_gcp h) (csx_gcr h) … H)
qed.
(* Advanced eliminators *****************************************************)
fact aaa_ind_csx_aux: ∀h,G,L,A. ∀Q:predicate term.
- (â\88\80T1. â¦\83G,Lâ¦\84 ⊢ T1 ⁝ A →
- (â\88\80T2. â¦\83G,Lâ¦\84 ⊢ T1 ⬈[h] T2 → (T1 ≛ T2 → ⊥) → Q T2) → Q T1
+ (â\88\80T1. â\9dªG,Lâ\9d« ⊢ T1 ⁝ A →
+ (â\88\80T2. â\9dªG,Lâ\9d« ⊢ T1 ⬈[h] T2 → (T1 ≛ T2 → ⊥) → Q T2) → Q T1
) →
- â\88\80T. â¦\83G,Lâ¦\84 â\8a¢ â¬\88*[h] ð\9d\90\92â¦\83Tâ¦\84 â\86\92 â¦\83G,Lâ¦\84 ⊢ T ⁝ A → Q T.
+ â\88\80T. â\9dªG,Lâ\9d« â\8a¢ â¬\88*[h] ð\9d\90\92â\9dªTâ\9d« â\86\92 â\9dªG,Lâ\9d« ⊢ T ⁝ A → Q T.
#h #G #L #A #Q #IH #T #H @(csx_ind … H) -T /4 width=5 by cpx_aaa_conf/
qed-.
lemma aaa_ind_csx: ∀h,G,L,A. ∀Q:predicate term.
- (â\88\80T1. â¦\83G,Lâ¦\84 ⊢ T1 ⁝ A →
- (â\88\80T2. â¦\83G,Lâ¦\84 ⊢ T1 ⬈[h] T2 → (T1 ≛ T2 → ⊥) → Q T2) → Q T1
+ (â\88\80T1. â\9dªG,Lâ\9d« ⊢ T1 ⁝ A →
+ (â\88\80T2. â\9dªG,Lâ\9d« ⊢ T1 ⬈[h] T2 → (T1 ≛ T2 → ⊥) → Q T2) → Q T1
) →
- â\88\80T. â¦\83G,Lâ¦\84 ⊢ T ⁝ A → Q T.
+ â\88\80T. â\9dªG,Lâ\9d« ⊢ T ⁝ A → Q T.
/5 width=9 by aaa_ind_csx_aux, aaa_csx/ qed-.
fact aaa_ind_csx_cpxs_aux: ∀h,G,L,A. ∀Q:predicate term.
- (â\88\80T1. â¦\83G,Lâ¦\84 ⊢ T1 ⁝ A →
- (â\88\80T2. â¦\83G,Lâ¦\84 ⊢ T1 ⬈*[h] T2 → (T1 ≛ T2 → ⊥) → Q T2) → Q T1
+ (â\88\80T1. â\9dªG,Lâ\9d« ⊢ T1 ⁝ A →
+ (â\88\80T2. â\9dªG,Lâ\9d« ⊢ T1 ⬈*[h] T2 → (T1 ≛ T2 → ⊥) → Q T2) → Q T1
) →
- â\88\80T. â¦\83G,Lâ¦\84 â\8a¢ â¬\88*[h] ð\9d\90\92â¦\83Tâ¦\84 â\86\92 â¦\83G,Lâ¦\84 ⊢ T ⁝ A → Q T.
+ â\88\80T. â\9dªG,Lâ\9d« â\8a¢ â¬\88*[h] ð\9d\90\92â\9dªTâ\9d« â\86\92 â\9dªG,Lâ\9d« ⊢ T ⁝ A → Q T.
#h #G #L #A #Q #IH #T #H @(csx_ind_cpxs … H) -T /4 width=5 by cpxs_aaa_conf/
qed-.
(* Basic_2A1: was: aaa_ind_csx_alt *)
lemma aaa_ind_csx_cpxs: ∀h,G,L,A. ∀Q:predicate term.
- (â\88\80T1. â¦\83G,Lâ¦\84 ⊢ T1 ⁝ A →
- (â\88\80T2. â¦\83G,Lâ¦\84 ⊢ T1 ⬈*[h] T2 → (T1 ≛ T2 → ⊥) → Q T2) → Q T1
+ (â\88\80T1. â\9dªG,Lâ\9d« ⊢ T1 ⁝ A →
+ (â\88\80T2. â\9dªG,Lâ\9d« ⊢ T1 ⬈*[h] T2 → (T1 ≛ T2 → ⊥) → Q T2) → Q T1
) →
- â\88\80T. â¦\83G,Lâ¦\84 ⊢ T ⁝ A → Q T.
+ â\88\80T. â\9dªG,Lâ\9d« ⊢ T ⁝ A → Q T.
/5 width=9 by aaa_ind_csx_cpxs_aux, aaa_csx/ qed-.