We prove that Ma\~n\'e's conjecture, as stated in {\em Lagrangian flows: the
dynamics of globally minimizing orbits}, Bol. Soc. Brasil. Mat. (N.S.) 28
(1997), no. 2, 141--153, contains another conjecture of Ma\~n\'e, stated in
{\em Generic properties and problems of minimizing measures of Lagrangian
systems} Nonlinearity 9 (1996) 273-310
