deffunc H₁( Nat) -> Element of SetPrimes = In ((primenumber $1),SetPrimes);
consider f being Function of NAT,SetPrimes such that
A1: for x being Element of NAT holds f . x = H₁(x) from FUNCT_2:sch 4();
take f ; :: thesis: for n being Nat holds f . n = primenumber n
let n be Nat; :: thesis: f . n = primenumber n
n in NAT by ORDINAL1:def 12;
then f . n = H₁(n) by A1;
hence f . n = primenumber n ; :: thesis: verum