x1=fan1=fr1 is a bijective function / isomorphism from x2=fan2 to x3=fan3, with inverse x4, in system / category x5; x1 has an inverse; x1 is a function that is injective and surjective; x2 and x3 are isomorphic; x1 is invertible.
x1 (plural of ordered pairs) is an exhaustive set (possibly infinite) of inputs/outputs defining a unary function which yields result x3 when given input x2; x1(x2) = x3