reserve x,y,y1,y2 for set;
reserve G for Group;
reserve a,b,c,d,g,h for Element of G;
reserve A,B,C,D for Subset of G;
reserve H,H1,H2,H3 for Subgroup of G;
reserve n for Nat;
reserve i for Integer;

theorem
  for G being strict Group holds G in Subgroups G
proof
  let G be strict Group;
  G is Subgroup of G by GROUP_2:54;
  hence thesis by Def1;
end;
