let X be non empty compact Subset of (TOP-REAL 2); :: thesis: LSeg ((W-min X),(W-max X)) c= LSeg ((SW-corner X),(NW-corner X))
A1: ( (SW-corner X) `1 = W-bound X & (NW-corner X) `1 = W-bound X ) by EUCLID:52;
A2: (W-max X) `2 <= (NW-corner X) `2 by Th30;
( (W-max X) `1 = W-bound X & (SW-corner X) `2 <= (W-max X) `2 ) by Th30, EUCLID:52;
then A3: W-max X in LSeg ((SW-corner X),(NW-corner X)) by A1, A2, GOBOARD7:7;
A4: (W-min X) `2 <= (NW-corner X) `2 by Th30;
( (W-min X) `1 = W-bound X & (SW-corner X) `2 <= (W-min X) `2 ) by Th30, EUCLID:52;
then W-min X in LSeg ((SW-corner X),(NW-corner X)) by A1, A4, GOBOARD7:7;
hence LSeg ((W-min X),(W-max X)) c= LSeg ((SW-corner X),(NW-corner X)) by A3, TOPREAL1:6; :: thesis: verum