reconsider z = 1 as Element of REAL by NUMBERS:19;
deffunc H₁( Nat) -> Element of Trivial-SigmaField REAL = {(z * $1)};
consider f being SetSequence of REAL such that
A1: for d being Element of NAT holds f . d = H₁(d) from FUNCT_2:sch 4();
take f ; :: thesis: for n being Nat holds f . n = {n}
let n be Nat; :: thesis: f . n = {n}
n in NAT by ORDINAL1:def 12;
then f . n = H₁(n) by A1
.= {n} ;
hence f . n = {n} ; :: thesis: verum