apply normalizes_ind
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x : A
⊢ normalizes R x → ∃ y, refl_trans_clos R x y ∧ normal R y
case a
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
x : A
⊢ ∀ (x : A),
    (∀ (y : A), R x y → ∃ y_1, refl_trans_clos R y y_1 ∧ normal R y_1) → ∃ y, refl_trans_clos R x y ∧ normal R y