∀ (X : AlgebraicGeometry.LocallyRingedSpace) (U : (TopologicalSpace.Opens ↑↑X.toPresheafedSpace)ᵒᵖ),
  (↑{ toFun := 0, map_one' := ⋯, map_mul' := ⋯ }).toFun 0 = (↑{ toFun := 0, map_one' := ⋯, map_mul' := ⋯ }).toFun 0