let r be Real; :: according to PARTFUN3:def 4 :: thesis: ( not r in rng (g * f) or 0 <= r )

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

then r in rng g by FUNCT_1:14;

hence 0 <= r by PARTFUN3:def 4; :: thesis: verum

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

then r in rng g by FUNCT_1:14;

hence 0 <= r by PARTFUN3:def 4; :: thesis: verum