Complementary symmetry was derived before under particular theories, and used to test those. Progressively general results were published. This paper proves the condition in complete generality, providing a one-line proof.

complementary symmetry, buying price, selling price, WTP, WTA
hdl.handle.net/1765/127112
Journal of Mathematical Psychology
Department of Applied Economics

Wakker, P.P. (2020). A One-Line Proof for Complementary Symmetry. Journal of Mathematical Psychology, in press. Retrieved from http://hdl.handle.net/1765/127112