deffunc H₁( Element of NAT ) -> Element of NAT = $1 + k;
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 Element of NAT holds f . n = n + k
let n be Nat; :: thesis: ( n is Element of REAL & n is Element of NAT implies f . n = n + k )
thus ( n is Element of REAL & n is Element of NAT implies f . n = n + k ) by A1; :: thesis: verum