
theorem Th2:
  for F being non empty set, f being non-empty FinSequence of bool
  F, i being Element of NAT st i in dom f holds f.i <> {}
proof
  let F be non empty set, f be non-empty FinSequence of bool F,
  i be Element of NAT;
  assume
A1: i in dom f;
  assume f.i = {};
  then {} in rng f by A1,FUNCT_1:3;
  hence thesis by RELAT_1:def 9;
end;
