reserve X,Y for set;
reserve R for domRing-like commutative Ring;
reserve c for Element of R;

theorem Th22:
  for R being associative well-unital non empty multLoopStr
  for Amp being AmpleSet of R holds
    (1.R in Amp) &
    (for a being Element of R ex z being Element of Amp st
      z is_associated_to a) &
    (for x,y being Element of Amp holds x <> y implies
      x is_not_associated_to y)
proof
  let R be associative well-unital non empty multLoopStr;
  let Amp be AmpleSet of R;
  Amp is Am of R by Def8;
  hence thesis by Def7,Def8;
end;
