reserve x, y for set;
reserve D for non empty set;
reserve UN for Universe;
reserve C for Category;
reserve O for non empty Subset of the carrier of C;
reserve G,H for AddGroup;
reserve V for Group_DOMAIN;

theorem Th30:
  for x being Element of GroupObjects(UN) holds x is strict AddGroup
proof
  let x be Element of GroupObjects(UN);
  consider u being object such that
  u in UN and
A1: GO u,x by Def22;
  ex x1,x2,x3,x4 being set st u = [x1,x2,x3,x4] & ex G being strict
AddGroup st x = G & x1 = the carrier of G & x2 = the addF of G & x3 = comp G &
  x4 = 0.G by A1;
  hence thesis;
end;
