(* Main properties with atomic arity assignment *****************************)
theorem aaa_csx (G) (L):
- â\88\80T,A. â\9dªG,Lâ\9d« â\8a¢ T â\81\9d A â\86\92 â\9dªG,Lâ\9d« ⊢ ⬈*𝐒 T.
+ â\88\80T,A. â\9d¨G,Lâ\9d© â\8a¢ T â\81\9d A â\86\92 â\9d¨G,Lâ\9d© ⊢ ⬈*𝐒 T.
#G #L #T #A #H
@(gcr_aaa … csx_gcp csx_gcr … H)
qed.
fact aaa_ind_csx_aux (G) (L):
∀A. ∀Q:predicate ….
- (â\88\80T1. â\9dªG,Lâ\9d« ⊢ T1 ⁝ A →
- (â\88\80T2. â\9dªG,Lâ\9d« â\8a¢ T1 â¬\88 T2 â\86\92 (T1 â\89\9b T2 → ⊥) → Q T2) → Q T1
+ (â\88\80T1. â\9d¨G,Lâ\9d© ⊢ T1 ⁝ A →
+ (â\88\80T2. â\9d¨G,Lâ\9d© â\8a¢ T1 â¬\88 T2 â\86\92 (T1 â\89\85 T2 → ⊥) → Q T2) → Q T1
) →
- â\88\80T. â\9dªG,Lâ\9d« â\8a¢ â¬\88*ð\9d\90\92 T â\86\92 â\9dªG,Lâ\9d« ⊢ T ⁝ A → Q T.
+ â\88\80T. â\9d¨G,Lâ\9d© â\8a¢ â¬\88*ð\9d\90\92 T â\86\92 â\9d¨G,Lâ\9d© ⊢ T ⁝ A → Q T.
#G #L #A #Q #IH #T #H @(csx_ind … H) -T /4 width=5 by cpx_aaa_conf/
qed-.
lemma aaa_ind_csx (G) (L):
∀A. ∀Q:predicate ….
- (â\88\80T1. â\9dªG,Lâ\9d« ⊢ T1 ⁝ A →
- (â\88\80T2. â\9dªG,Lâ\9d« â\8a¢ T1 â¬\88 T2 â\86\92 (T1 â\89\9b T2 → ⊥) → Q T2) → Q T1
+ (â\88\80T1. â\9d¨G,Lâ\9d© ⊢ T1 ⁝ A →
+ (â\88\80T2. â\9d¨G,Lâ\9d© â\8a¢ T1 â¬\88 T2 â\86\92 (T1 â\89\85 T2 → ⊥) → Q T2) → Q T1
) →
- â\88\80T. â\9dªG,Lâ\9d« ⊢ T ⁝ A → Q T.
+ â\88\80T. â\9d¨G,Lâ\9d© ⊢ T ⁝ A → Q T.
/5 width=9 by aaa_ind_csx_aux, aaa_csx/ qed-.
fact aaa_ind_csx_cpxs_aux (G) (L):
∀A. ∀Q:predicate ….
- (â\88\80T1. â\9dªG,Lâ\9d« ⊢ T1 ⁝ A →
- (â\88\80T2. â\9dªG,Lâ\9d« â\8a¢ T1 â¬\88* T2 â\86\92 (T1 â\89\9b T2 → ⊥) → Q T2) → Q T1
+ (â\88\80T1. â\9d¨G,Lâ\9d© ⊢ T1 ⁝ A →
+ (â\88\80T2. â\9d¨G,Lâ\9d© â\8a¢ T1 â¬\88* T2 â\86\92 (T1 â\89\85 T2 → ⊥) → Q T2) → Q T1
) →
- â\88\80T. â\9dªG,Lâ\9d« â\8a¢ â¬\88*ð\9d\90\92 T â\86\92 â\9dªG,Lâ\9d« ⊢ T ⁝ A → Q T.
+ â\88\80T. â\9d¨G,Lâ\9d© â\8a¢ â¬\88*ð\9d\90\92 T â\86\92 â\9d¨G,Lâ\9d© ⊢ T ⁝ A → Q T.
#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 (G) (L):
∀A. ∀Q:predicate ….
- (â\88\80T1. â\9dªG,Lâ\9d« ⊢ T1 ⁝ A →
- (â\88\80T2. â\9dªG,Lâ\9d« â\8a¢ T1 â¬\88* T2 â\86\92 (T1 â\89\9b T2 → ⊥) → Q T2) → Q T1
+ (â\88\80T1. â\9d¨G,Lâ\9d© ⊢ T1 ⁝ A →
+ (â\88\80T2. â\9d¨G,Lâ\9d© â\8a¢ T1 â¬\88* T2 â\86\92 (T1 â\89\85 T2 → ⊥) → Q T2) → Q T1
) →
- â\88\80T. â\9dªG,Lâ\9d« ⊢ T ⁝ A → Q T.
+ â\88\80T. â\9d¨G,Lâ\9d© ⊢ T ⁝ A → Q T.
/5 width=9 by aaa_ind_csx_cpxs_aux, aaa_csx/ qed-.