deffunc H₁( Element of L) -> Element of the carrier of L = eval (p,$1);
consider f being Function of the carrier of L, the carrier of L such that
A1: for x being Element of L holds f . x = H₁(x) from FUNCT_2:sch 4();
reconsider f = f as Function of L,L ;
take f ; :: thesis: for x being Element of L holds f . x = eval (p,x)
thus for x being Element of L holds f . x = eval (p,x) by A1; :: thesis: verum