(* Basic_2A1: was: cpcs_ind_dx *)
lemma cpcs_ind_sn (h) (G) (L) (T2):
- ∀R:predicate term. R T2 →
- (∀T1,T. ⦃G, L⦄ ⊢ T1 ⬌[h] T → ⦃G, L⦄ ⊢ T ⬌*[h] T2 → R T → R T1) →
- ∀T1. ⦃G, L⦄ ⊢ T1 ⬌*[h] T2 → R T1.
+ ∀Q:predicate term. Q T2 →
+ (∀T1,T. ⦃G, L⦄ ⊢ T1 ⬌[h] T → ⦃G, L⦄ ⊢ T ⬌*[h] T2 → Q T → Q T1) →
+ ∀T1. ⦃G, L⦄ ⊢ T1 ⬌*[h] T2 → Q T1.
normalize /3 width=6 by TC_star_ind_dx/
qed-.
(* Basic_2A1: was: cpcs_ind *)
lemma cpcs_ind_dx (h) (G) (L) (T1):
- ∀R:predicate term. R T1 →
- (∀T,T2. ⦃G, L⦄ ⊢ T1 ⬌*[h] T → ⦃G, L⦄ ⊢ T ⬌[h] T2 → R T → R T2) →
- ∀T2. ⦃G, L⦄ ⊢ T1 ⬌*[h] T2 → R T2.
+ ∀Q:predicate term. Q T1 →
+ (∀T,T2. ⦃G, L⦄ ⊢ T1 ⬌*[h] T → ⦃G, L⦄ ⊢ T ⬌[h] T2 → Q T → Q T2) →
+ ∀T2. ⦃G, L⦄ ⊢ T1 ⬌*[h] T2 → Q T2.
normalize /3 width=6 by TC_star_ind/
qed-.