deffunc H₁( Element of Bags X) -> Element of the carrier of L = (p . $1) * a;
consider f being Function of (Bags X), the carrier of L such that
A4: for x being Element of Bags X holds f . x = H₁(x) from FUNCT_2:sch 4();
reconsider f = f as Function of (Bags X),L ;
reconsider f = f as Series of X,L ;
reconsider f = f as Series of X,L ;
take f ; :: thesis: for b being bag of X holds f . b = (p . b) * a
let x be bag of X; :: thesis: f . x = (p . x) * a
x in Bags X by PRE_POLY:def 12;
hence f . x = (p . x) * a by A4; :: thesis: verum