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
  mlt(i|->c1,i|->c2) = i|->(c1*c2)
proof
  reconsider s1=c1, s2=c2 as Element of COMPLEX by XCMPLX_0:def 2;
  mlt(i|->s1,i|->s2) = s1*(i|->s2) by Th27
    .= i|->(c1*c2) by Th22;
  hence thesis;
end;
