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 (-) B)\/(Y (-) B) c= (X\/Y) (-) B
proof
  let x be object;
  assume x in (X (-) B)\/(Y (-) B);
  then x in X (-) B or x in Y (-) B by XBOOLE_0:def 3;
  then consider y being Point of T such that
A1: x=y & B+y c= X or x=y & B+y c= Y;
  B+y c= X \/ Y
  by A1,XBOOLE_0:def 3;
  hence thesis by A1;
end;
