deffunc H₁( Element of NAT ) -> Element of NAT = ($1 + a) ! ;
consider h being Function of NAT,REAL such that
A1: for n being Element of NAT holds h . n = H₁(n) from FUNCT_2:sch 4();
take h ; :: thesis: for n being Element of NAT holds h . n = (n + a) !
let n be Element of NAT ; :: thesis: h . n = (n + a) !
thus h . n = (n + a) ! by A1; :: thesis: verum