We prove that the generalized cancellation axiom for incomplete comparative probability relations introduced by Ríos Insua (Theory Decis 33:83–100, 1992) and Alon and Lehrer (J Econ Theory 151:476–492, 2014) is stronger than the standard cancellation axiom for complete comparative probability relations introduced by Scott (J Math Psychol 1:233–247, 1964), relative to their other axioms for comparative probability in both the finite and infinite cases. This result has been suggested but not proved in the previous literature
