let r be Real; :: according to PARTFUN3:def 2 :: thesis: ( not r in rng (g * f) or not 0 <= r )

assume r in rng (g * f) ; :: thesis: not 0 <= r

then r in rng g by FUNCT_1:14;

hence 0 > r by PARTFUN3:def 2; :: thesis: verum

assume r in rng (g * f) ; :: thesis: not 0 <= r

then r in rng g by FUNCT_1:14;

hence 0 > r by PARTFUN3:def 2; :: thesis: verum