. intro h w x
  have := h (w * x)
  rw [<- Word.monoid.mul_assoc] at this
  rw [<- Word.monoid.mul_assoc] at this
  assumption
case mp
α : Type u_1
L : Language α
u v : Word α
⊢ u ≃( L ) v → ∀ (x : Word α), u * x ≃( L ) v * x

case mpr
α : Type u_1
L : Language α
u v : Word α
⊢ (∀ (x : Word α), u * x ≃( L ) v * x) → u ≃( L ) v
case mpr
α : Type u_1
L : Language α
u v : Word α
⊢ (∀ (x : Word α), u * x ≃( L ) v * x) → u ≃( L ) v