intros P IH x norm
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
⊢ ∀ (P : A → Prop), (∀ (x : A), (∀ (y : A), R x y → P y) → P x) → ∀ (x : A), normalizes R x → P x
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
P : A → Prop
IH : ∀ (x : A), (∀ (y : A), R x y → P y) → P x
x : A
norm : normalizes R x
⊢ P x