reserve x,y,z, X,Y,Z for set,
  n for Element of NAT;
reserve A for set,
  D for non empty set,
  a,b,c,l,r for Element of D,
  o,o9 for BinOp of D,
  f,g,h for Function of A,D;
reserve G for non empty multMagma;

theorem Th20:
  for f,g being Element of .:(G,X) st
   for x being object st x in X holds f.x = g.x holds f = g
proof
  let f,g be Element of .:(G,X);
  dom f = X & dom g = X by Th19;
  hence thesis by FUNCT_1:2;
end;
