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 Th10:
  B1 c= B2 implies X (-) B2 c= X (-) B1 & X (+) B1 c= X (+) B2
proof
  assume
A1: B1 c= B2;
  thus X (-) B2 c= X (-) B1
  proof
    let p be object;
    assume p in X (-) B2;
    then consider p1 being Point of T such that
A2: p = p1 and
A3: B2+p1 c= X;
    B1+p1 c= B2 + p1 by A1,Th3;
    then B1+p1 c= X by A3;
    hence thesis by A2;
  end;
  let p be object;
  assume p in X (+) B1;
  then ex x,b being Point of T st p = x+b & x in X & b in B1;
  hence thesis by A1;
end;
