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
  X (@) (B2,B1) = (X` (&) (B1,B2))`
proof
  (X` (&) (B1,B2))` =((X \ ((X` (-) B1) /\ ((X`)` (-) B2)))`)` by SUBSET_1:14
    .=X \ (X (*) (B2,B1));
  hence thesis;
end;
