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;
reserve t,s,r1 for Real;
reserve n for Element of NAT;
reserve X,Y,B1,B2 for Subset of TOP-REAL n;
reserve x,y for Point of TOP-REAL n;

theorem
  B1 = {} implies X (*) (B1,B2) = X` (-) B2
proof
  assume B1 = {};
  then X (*) (B1,B2) = (X` (-) B2) /\ the carrier of TOP-REAL n by Th8;
  hence thesis by XBOOLE_1:28;
end;
