is there a built-in function to check if a list of things all cause a function to give the same result?

if f returns booleans, the function I’m thinking of should give the same result as: (lambda (f x*) (or (andmap f x*) (not (ormap f x*))))

or, for any f, the result should be the same as (lambda (f x*) (= 1 (set-count (list->set (map f x*)))))