let C be Subset of (TOP-REAL 2); LSeg (NW-corner C),(NE-corner C) c= L~ (SpStSeq C)
A1:
(LSeg (NW-corner C),(NE-corner C)) \/ (LSeg (NE-corner C),(SE-corner C)) c= ((LSeg (NW-corner C),(NE-corner C)) \/ (LSeg (NE-corner C),(SE-corner C))) \/ ((LSeg (SE-corner C),(SW-corner C)) \/ (LSeg (SW-corner C),(NW-corner C)))
by XBOOLE_1:7;
LSeg (NW-corner C),(NE-corner C) c= (LSeg (NW-corner C),(NE-corner C)) \/ (LSeg (NE-corner C),(SE-corner C))
by XBOOLE_1:7;
then
LSeg (NW-corner C),(NE-corner C) c= ((LSeg (NW-corner C),(NE-corner C)) \/ (LSeg (NE-corner C),(SE-corner C))) \/ ((LSeg (SE-corner C),(SW-corner C)) \/ (LSeg (SW-corner C),(NW-corner C)))
by A1, XBOOLE_1:1;
hence
LSeg (NW-corner C),(NE-corner C) c= L~ (SpStSeq C)
by SPRECT_1:43; verum