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|->(c1*c2)) = (Product (i|->c1))*(Product (i|->c2))
proof
  reconsider s1=c1, s2=c2, ss = c1*c2 as Element of COMPLEX by XCMPLX_0:def 2;
  Product (i|->(ss)) = multcomplex$$(i|->multcomplex.(s1,s2))
  by BINOP_2:def 5
    .= multcomplex.(multcomplex$$(i|->s1),multcomplex$$(i|->s2)) by SETWOP_2:36
    .= (Product (i|->s1))*(Product (i|->s2)) by BINOP_2:def 5;
  hence thesis;
end;
