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 (+) (Y (-) Z) c= (X (+) Y) (-) Z
proof
  let x be object;
  assume x in X (+) (Y (-) Z);
  then consider a,b being Point of T such that
A1: x=a+b and
A2: a in X and
A3: b in Y (-) Z;
  ex c being Point of T st b=c & Z+c c= Y by A3;
  then Z+b+a c= Y+a by Th3;
  then
A4: Z+(b+a) c= Y+a by Th16;
  Y+a c= Y (+) X by A2,Th19;
  then Z+(b+a) c= Y (+) X by A4;
  then x in (Y (+) X) (-) Z by A1;
  hence thesis by Th12;
end;
