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

theorem Th29:
  for Amp being AmpleSet of R for a,b being Element of R holds
  gcd(a,b,Amp) = gcd(b,a,Amp)
proof
  let Amp be AmpleSet of R;
  let A,B be Element of R;
  set D = gcd(A,B,Amp);
A1: D divides A & for z being Element of R st z divides B & z divides A
  holds z divides D by Def12;
  D in Amp & D divides B by Def12;
  hence thesis by A1,Def12;
end;
