let x be set ; :: according to VALUED_0:def 9 :: thesis: ( not x in proj1 (a * b) or not (a * b) . x is V34() )
assume x in dom (a * b) ; :: thesis: (a * b) . x is V34()
(a * b) . x = a * (b . x) by Def2;
hence (a * b) . x is V34() ; :: thesis: verum