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 Th19:
  a |^ 1_G = a
proof
  thus a |^ 1_G = (1_G)" * a by GROUP_1:def 4
    .= 1_G * a by GROUP_1:8
    .= a by GROUP_1:def 4;
end;
