deffunc H₁( Real) -> Element of REAL = Im (Sum (($1 * <i>) ExpSeq));
consider f being Function of REAL,REAL such that
A1: for x being Element of REAL holds f . x = H₁(x) from FUNCT_2:sch 4();
take f ; :: thesis: for d being Real holds f . d = Im (Sum ((d * <i>) ExpSeq))
let x be Real; :: thesis: f . x = Im (Sum ((x * <i>) ExpSeq))
reconsider x = x as Element of REAL by XREAL_0:def 1;
f . x = H₁(x) by A1;
hence f . x = Im (Sum ((x * <i>) ExpSeq)) ; :: thesis: verum