∀ {X Y : HeytAlg} (f : X ⟶ Y) (a b : ↑X),
  { toFun := ⇑(HeytAlg.Hom.hom f), map_sup' := ⋯, map_inf' := ⋯ }.toFun (a ⊓ b) =
    { toFun := ⇑(HeytAlg.Hom.hom f), map_sup' := ⋯, map_inf' := ⋯ }.toFun a ⊓
      { toFun := ⇑(HeytAlg.Hom.hom f), map_sup' := ⋯, map_inf' := ⋯ }.toFun b