have eq_d : X.d = w := by
  apply normal_red RX <;> aesop
case intro.intro
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
w : X
h1 : refl_trans_clos RX X.a w
h2 : refl_trans_clos RX X.d w
eq_a : X.a = w
⊢ False
case intro.intro
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
w : X
h1 : refl_trans_clos RX X.a w
h2 : refl_trans_clos RX X.d w
eq_a : X.a = w
eq_d : X.d = w
⊢ False