deffunc H₁( Element of Bags X) -> Element of the carrier of L = a * (p . $1);
consider f being Function of (Bags X), the carrier of L such that
A1: 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 = a * (p . b)
let x be bag of X; :: thesis: f . x = a * (p . x)
x in Bags X by PRE_POLY:def 12;
hence f . x = a * (p . x) by A1; :: thesis: verum