
theorem Th1:
  for I be set, F be Group-Family of I holds
  for i be object st i in I holds F.i is Group
  proof
    let I be set;
    let F be Group-Family of I;
    let i be object;
    assume
    A1: i in I; then
    ex Fi be Group-like non empty multMagma st Fi = F.i by GROUP_7:def 3;
    hence thesis by A1;
  end;
