reserve s for set,
  i,j for Nat,
  c,c1,c2,c3 for Complex,
  F,F1,F2 for complex-valued FinSequence,
  R,R1,R2 for i-element complex-valued FinSequence;

theorem
  Product ((i+j) |->c) = (Product (i|->c))*(Product (j|->c))
proof
  reconsider s=c as Element of COMPLEX by XCMPLX_0:def 2;
  Product ((i+j) |->s) =
    multcomplex.(multcomplex$$(i|->s),multcomplex$$(j|->s)) by SETWOP_2:26
    .= (Product (i|->s))*(Product (j|->s)) by BINOP_2:def 5;
  hence thesis;
end;
