
theorem Th5:
  for I being non empty set
  for F being Group-yielding ManySortedSet of I
  for i being Element of I
  holds F.i is Group
proof
  let I be non empty set;
  let F be Group-yielding ManySortedSet of I;
  let i be Element of I;
  i in I & dom F = I by PARTFUN1:def 2;
  then F.i in rng F by FUNCT_1:3;
  hence F.i is Group by Def1;
end;
