(* 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❫ ⊢ ⬈*𝐒[h] 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
- ) →
- ∀T. ❪G,L❫ ⊢ ⬈*[h] 𝐒❪T❫ → ❪G,L❫ ⊢ T ⁝ A → Q T.
+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
+ ) →
+ ∀T. ❪G,L❫ ⊢ ⬈*𝐒[h] 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
- ) →
- ∀T. ❪G,L❫ ⊢ T ⁝ A → Q T.
+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
+ ) →
+ ∀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
- ) →
- ∀T. ❪G,L❫ ⊢ ⬈*[h] 𝐒❪T❫ → ❪G,L❫ ⊢ T ⁝ A → Q T.
+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❫ ⊢ ⬈*𝐒[h] 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
- ) →
- ∀T. ❪G,L❫ ⊢ T ⁝ A → Q T.
+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
+ ) →
+ ∀T. ❪G,L❫ ⊢ T ⁝ A → Q T.
/5 width=9 by aaa_ind_csx_cpxs_aux, aaa_csx/ qed-.