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 Th24:
  a |^ g |^ h = a |^ (g * h)
proof
  thus a |^ g |^ h = h" * (g" * a) * g * h by GROUP_1:def 3
    .= h" * g" * a * g * h by GROUP_1:def 3
    .= (g * h)" * a * g * h by GROUP_1:17
    .= a |^ (g * h) by GROUP_1:def 3;
end;
