deffunc H₁( Nat) -> Element of NAT = In (($1 + k),NAT);
consider f being sequence of NAT 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 = n + k
let n be Nat; :: thesis: f . n = n + k
n in NAT by ORDINAL1:def 12;
then f . n = H₁(n) by A1;
hence f . n = n + k ; :: thesis: verum