let x be object ; :: according to VALUED_0:def 12 :: thesis: ( not x in dom (r (#) f) or (r (#) f) . x is natural )
assume x in dom (r (#) f) ; :: thesis: (r (#) f) . x is natural
then (r (#) f) . x = r * (f . x) by Def5;
hence (r (#) f) . x is natural ; :: thesis: verum