deffunc H₁( Nat) -> Element of the carrier of Y = (H . $1) . x;
consider f being sequence of the carrier of Y such that
A1: for n being Element of NAT holds f . n = H₁(n) from FUNCT_2:sch 4();
take f ; :: thesis: for n being Nat holds f . n = (H . n) . x
let n be Nat; :: thesis: f . n = (H . n) . x
n in NAT by ORDINAL1:def 12;
hence f . n = (H . n) . x by A1; :: thesis: verum