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
  B c= C implies X (o) B c= (X (+) C) (-) B
proof
  assume B c= C;
  then
A1: X (+) B c= X (+) C by Th10;
  let x be object;
  assume x in X (o) B;
  then consider x2 being Point of T such that
A2: x=x2 and
A3: B+x2 c= X (+) B;
  B+x2 c= X (+) C by A3,A1;
  hence thesis by A2;
end;
