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 Th17:
  (1_G) |^ a = 1_G
proof
  thus (1_G) |^ a = a" * a by GROUP_1:def 4
    .= 1_G by GROUP_1:def 5;
end;
