let M be non empty commutative multMagma ; :: thesis: ( M is left_mult-cancelable implies M is right_mult-cancelable )
assume A15: M is left_mult-cancelable ; :: thesis: M is right_mult-cancelable
let x, y, z be Element of M; :: according to ALGSTR_0:def 21,ALGSTR_0:def 24 :: thesis: ( not y * x = z * x or y = z )
assume y * x = z * x ; :: thesis: y = z
hence y = z by A15, ALGSTR_0:def 20; :: thesis: verum