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

theorem Th31:
  for Amp being AmpleSet of R holds gcd(0.R,0.R,Amp) = 0.R
proof
  let Amp be AmpleSet of R;
  gcd(0.R,0.R,Amp) = NF(0.R,Amp) by Th30;
  hence thesis by Th25;
end;
