let x be object ; :: according to VALUED_0:def 12 :: thesis: ( not x in dom (max (b1,b2)) or not (max (b1,b2)) . x is natural )
set f = max (b1,b2);
assume x in dom (max (b1,b2)) ; :: thesis: (max (b1,b2)) . x is natural
( b1 . x <= b2 . x or b1 . x > b2 . x ) ;
hence (max (b1,b2)) . x is natural by Def4; :: thesis: verum