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 Th26:
  a" |^ b = (a |^ b)"
proof
  thus a" |^ b = (a * b)" * b by GROUP_1:17
    .= (a * b)" * b""
    .= (b" * (a * b))" by GROUP_1:17
    .= (a |^ b)" by GROUP_1:def 3;
end;
