let r be Real; :: according to PARTFUN3:def 3 :: thesis: ( not r in rng (g * f) or r <= 0 )

assume r in rng (g * f) ; :: thesis: r <= 0

then r in rng g by FUNCT_1:14;

hence 0 >= r by PARTFUN3:def 3; :: thesis: verum

assume r in rng (g * f) ; :: thesis: r <= 0

then r in rng g by FUNCT_1:14;

hence 0 >= r by PARTFUN3:def 3; :: thesis: verum