let X be non empty compact Subset of (TOP-REAL 2); :: thesis: LSeg (S-min X),(S-max X) c= LSeg (SW-corner X),(SE-corner X)
A1: ( (SW-corner X) `2 = S-bound X & (SE-corner X) `2 = S-bound X ) by EUCLID:56;
A2: (S-max X) `1 <= (SE-corner X) `1 by Th117;
( (S-max X) `2 = S-bound X & (SW-corner X) `1 <= (S-max X) `1 ) by Th117, EUCLID:56;
then A3: S-max X in LSeg (SW-corner X),(SE-corner X) by A1, A2, GOBOARD7:9;
A4: (S-min X) `1 <= (SE-corner X) `1 by Th117;
( (S-min X) `2 = S-bound X & (SW-corner X) `1 <= (S-min X) `1 ) by Th117, EUCLID:56;
then S-min X in LSeg (SW-corner X),(SE-corner X) by A1, A4, GOBOARD7:9;
hence LSeg (S-min X),(S-max X) c= LSeg (SW-corner X),(SE-corner X) by A3, TOPREAL1:12; :: thesis: verum