let r be Real; :: according to PARTFUN3:def 1 :: thesis: ( not r in rng (g * f) or not r <= 0 )

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

then r in rng g by FUNCT_1:14;

hence 0 < r by PARTFUN3:def 1; :: thesis: verum

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

then r in rng g by FUNCT_1:14;

hence 0 < r by PARTFUN3:def 1; :: thesis: verum