
theorem Th7:
  for X be set, F be FinSequence of X, i be Nat st i in dom F holds
  F.i c= union rng F & F.i /\ union rng F = F.i
proof
  let X be set, F be FinSequence of X, i be Nat;
  assume
A1: i in dom F;
  hence F.i c= union rng F by FUNCT_1:3,ZFMISC_1:74;
  F.i in rng F by A1,FUNCT_1:3;
  hence thesis by XBOOLE_1:28,ZFMISC_1:74;
end;
