reserve T for non empty Abelian
  add-associative right_zeroed right_complementable RLSStruct,
  X,Y,Z,B,C,B1,B2 for Subset of T,
  x,y,p for Point of T;

theorem
  (X (O) B) (O) B = X (O) B
proof
  thus (X (O) B) (O) B c= X (O) B by Th41;
  let x be object;
  assume x in X (O) B;
  then consider x1,b1 being Point of T such that
A1: x=x1+b1 and
A2: x1 in X (-) B and
A3: b1 in B;
  consider x2 being Point of T such that
A4: x1=x2 and
A5: B+x2 c= X by A2;
  (B+x2) (O) B c= X (O) B by A5,Th45;
  then (B (O) B)+x2 c= X (O) B by Th46;
  then B+x2 c= X (O) B by Th42;
  then x1 in {x4 where x4 is Point of T:B+x4 c= X (O) B}by A4;
  hence thesis by A1,A3;
end;
