St. like "strict-independence" (maybe property?) of some constructors would be quite useful; I am having the following problem: I proved that Image F (for F being homomorphism of structures U1,U2) preserves some property (monotonicity) and now I would like to prove that for U1,U2 being isomorphic, the monotonicity of U1 is equivalent to monotonicity of U2. So I want to use Image F = U2, but this works only if U2 is strict. But in many cases (e.g. my "monotonicity"), the property is "strict-independent", in the sense that if the fields of two structures agree, the property is preserved. It is painful to prove such independence by hand for any necessary constructor, and I have no idea how to do such thing by schemes. Any ideas? -- JosefUrban - 08 Aug 2002