∀ {α β : BddLat} (e : ↑α.toLat ≃o ↑β.toLat) (a b : ↑α.1),
  { toFun := ⇑e, map_sup' := ⋯, map_inf' := ⋯ }.toFun (a ⊔ b) =
    { toFun := ⇑e, map_sup' := ⋯, map_inf' := ⋯ }.toFun a ⊔ { toFun := ⇑e, map_sup' := ⋯, map_inf' := ⋯ }.toFun b