(* Main properties with atomic arity assignment *****************************)
-theorem aaa_csx: ∀h,G,L,T,A. ⦃G, L⦄ ⊢ T ⁝ A → ⦃G, L⦄ ⊢ ⬈*[h] 𝐒⦃T⦄.
+theorem aaa_csx: ∀h,G,L,T,A. ⦃G,L⦄ ⊢ T ⁝ A → ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃T⦄.
#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.
- (∀T1. ⦃G, L⦄ ⊢ T1 ⁝ A →
- (∀T2. ⦃G, L⦄ ⊢ T1 ⬈[h] T2 → (T1 ≛ T2 → ⊥) → Q T2) → Q T1
+ (∀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.
+ ∀T. ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃T⦄ → ⦃G,L⦄ ⊢ 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.
- (∀T1. ⦃G, L⦄ ⊢ T1 ⁝ A →
- (∀T2. ⦃G, L⦄ ⊢ T1 ⬈[h] T2 → (T1 ≛ T2 → ⊥) → Q T2) → Q T1
+ (∀T1. ⦃G,L⦄ ⊢ T1 ⁝ A →
+ (∀T2. ⦃G,L⦄ ⊢ T1 ⬈[h] T2 → (T1 ≛ T2 → ⊥) → Q T2) → Q T1
) →
- ∀T. ⦃G, L⦄ ⊢ T ⁝ A → Q T.
+ ∀T. ⦃G,L⦄ ⊢ 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.
- (∀T1. ⦃G, L⦄ ⊢ T1 ⁝ A →
- (∀T2. ⦃G, L⦄ ⊢ T1 ⬈*[h] T2 → (T1 ≛ T2 → ⊥) → Q T2) → Q T1
+ (∀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.
+ ∀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/
qed-.
(* Basic_2A1: was: aaa_ind_csx_alt *)
lemma aaa_ind_csx_cpxs: ∀h,G,L,A. ∀Q:predicate term.
- (∀T1. ⦃G, L⦄ ⊢ T1 ⁝ A →
- (∀T2. ⦃G, L⦄ ⊢ T1 ⬈*[h] T2 → (T1 ≛ T2 → ⊥) → Q T2) → Q T1
+ (∀T1. ⦃G,L⦄ ⊢ T1 ⁝ A →
+ (∀T2. ⦃G,L⦄ ⊢ T1 ⬈*[h] T2 → (T1 ≛ T2 → ⊥) → Q T2) → Q T1
) →
- ∀T. ⦃G, L⦄ ⊢ T ⁝ A → Q T.
+ ∀T. ⦃G,L⦄ ⊢ T ⁝ A → Q T.
/5 width=9 by aaa_ind_csx_cpxs_aux, aaa_csx/ qed-.