deffunc H₁( Element of NAT ) -> Element of X = s . ($1 + k);
consider f being sequence of X 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 = s . (n + k)
let n be Nat; :: thesis: f . n = s . (n + k)
n in NAT by ORDINAL1:def 13;
hence f . n = s . (n + k) by A1; :: thesis: verum