deffunc H₁( object ) -> set = { F where F is Filter of L : ( F is prime & $1 in F ) } ;
consider f being Function such that
A1: dom f = the carrier of L and
A2: for x being object st x in the carrier of L holds
f . x = H₁(x) from FUNCT_1:sch 3();
take f ; :: thesis: ( dom f = the carrier of L & ( for a being Element of L holds f . a = { F where F is Filter of L : ( F is prime & a in F ) } ) )
thus ( dom f = the carrier of L & ( for a being Element of L holds f . a = { F where F is Filter of L : ( F is prime & a in F ) } ) ) by A1, A2; :: thesis: verum