theorem Th49:
  o is commutative implies o.:^2 is commutative
proof
  assume
A1: o is commutative;
  let x,y be Subset of D;
  thus (o.:^2).(x,y) = o.:[:x,y:] by Th44
    .= o.:[:y,x:] by A1,Th47
    .= (o.:^2).(y,x) by Th44;
end;
