apply ind_normalizing
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
norm : normalizing R
⊢ normalizing fun x x_1 => trans_clos R x x_1
case a
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
norm : normalizing R
⊢ ∀ (P : A → Prop), (∀ (x : A), (∀ (y : A), trans_clos R x y → P y) → P x) → ∀ (x : A), P x