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 Th27:
  mlt(i|->c,R) = c*R
proof
A1: R is i-element FinSequence of COMPLEX by FINSEQ_1:102;
  reconsider s=c as Element of COMPLEX by XCMPLX_0:def 2;
  mlt(i|->s,R) = multcomplex[;](s,R) by A1,FINSEQOP:20
    .= c*R by A1,FINSEQOP:22;
  hence thesis;
end;
