deffunc H₁( Nat) -> Element of the carrier of X = (1r / ($1 !)) * (z #N $1);
consider s being sequence of X such that
A1: for n being Element of NAT holds s . n = H₁(n) from FUNCT_2:sch 4();
take s ; :: thesis: for n being Nat holds s . n = (1r / (n !)) * (z #N n)
let n be Nat; :: thesis: s . n = (1r / (n !)) * (z #N n)
n in NAT by ORDINAL1:def 12;
hence s . n = (1r / (n !)) * (z #N n) by A1; :: thesis: verum