theorem
  [:X1 \/ X2, Y1 \/ Y2:] = [:X1,Y1:] \/ [:X1,Y2:] \/ [:X2,Y1:] \/ [:X2, Y2:]
proof
  thus [:X1 \/ X2, Y1 \/ Y2:] = [:X1, Y1 \/ Y2:] \/ [:X2, Y1 \/ Y2:] by Th96
    .= [:X1,Y1:] \/ [:X1,Y2:] \/ [:X2,Y1 \/ Y2:] by Th96
    .= [:X1,Y1:] \/ [:X1,Y2:] \/ ([:X2,Y1:] \/ [:X2,Y2:]) by Th96
    .= [:X1,Y1:] \/ [:X1,Y2:] \/ [:X2,Y1:] \/ [:X2,Y2:] by XBOOLE_1:4;
end;
