
theorem EMP:
  for f be complex-valued FinSequence holds 0(#)f = (len f)|-> 0
  proof
    let f be complex-valued FinSequence;
    A1: dom (0(#)f) = dom f by VALUED_1:def 5
    .= Seg len ((len f)|-> 0) by FINSEQ_1:def 3
    .= dom ((len f)|-> 0);
    for c be Nat st c in dom (0(#)f) holds (0(#)f).c = ((len f)|-> 0).c;
    hence thesis by A1,FINSEQ_1:13;
  end;
