reserve i,j,n,k for Nat,
  a for Element of COMPLEX,
  R1,R2 for Element of i-tuples_on COMPLEX;

theorem Th17:
  for F1,F2 being FinSequence of COMPLEX,i being Nat holds i in
  dom mlt(F1,F2) implies mlt(F1,F2).i = F1.i * F2.i
proof
  let F1,F2 be FinSequence of COMPLEX,i be Nat;
  set r1 = F1.i, r2 = F2.i;
  assume i in dom mlt(F1,F2);
  then mlt(F1,F2).i = multcomplex.(r1,r2) by FUNCOP_1:22;
  hence thesis by BINOP_2:def 5;
end;
