(* Mike Stannett Feb 2023 *) section ‹ AXIOM: AxEField › text ‹This theory defines the axiom AxEField, which states that the linearly ordered field of quantities is Euclidean, i.e. that all non-negative values have square roots in the field. › theory AxEField imports Sorts begin class axEField = Quantities begin abbreviation axEField :: "'a ⇒ bool" where "axEField x ≡ (x ≥ 0) ⟶ hasRoot x" end (* of class axEField *) class AxEField = axEField + assumes AxEField: "∀ x . axEField x" begin end (* of class AxEField *) end (* of theory AxEField *)