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 Th14:
  (X+p) (-) Y = (X (-) Y)+p
proof
  thus (X+p) (-) Y c= (X (-) Y)+p
  proof
    let x be object;
    assume x in (X+p) (-) Y;
    then consider y being Point of T such that
A1: x = y and
A2: Y+y c= X+p;
    Y+(y-p) c= X by A2,Th13;
    then y-p in {y1 where y1 is Point of T:Y+y1 c= X};
    then (y-p)+p in {q+p where q is Point of T:q in X (-) Y};
    hence thesis by A1,Lm2;
  end;
  let x be object;
  assume x in (X (-) Y)+p;
  then consider y being Point of T such that
A3: x = y+p and
A4: y in X (-) Y;
  reconsider x as Point of T by A3;
  x-p = y & ex y2 being Point of T st y = y2 & Y+y2 c= X by A3,A4,Lm2;
  then Y + x c= X + p by Th13;
  hence thesis;
end;
