reserve T for non empty RelStr,
  A,B for Subset of T,
  x,x2,y,z for Element of T;

theorem
  (A /\ B)^b c= (A^b) /\ (B^b)
proof
  let x be object;
  assume
A1: x in (A /\ B)^b;
  then reconsider px=x as Point of T;
A2: U_FT px meets (A /\ B) by A1,FIN_TOPO:8;
  then U_FT px meets B by XBOOLE_1:74;
  then
A3: x in B^b by FIN_TOPO:8;
  U_FT px meets A by A2,XBOOLE_1:74;
  then x in A^b by FIN_TOPO:8;
  hence thesis by A3,XBOOLE_0:def 4;
end;
