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:52;
A2: (S-max X) `1 <= (SE-corner X) `1 by Th54;
( (S-max X) `2 = S-bound X & (SW-corner X) `1 <= (S-max X) `1 ) by Th54, EUCLID:52;
then A3: S-max X in LSeg ((SW-corner X),(SE-corner X)) by A1, A2, GOBOARD7:8;
A4: (S-min X) `1 <= (SE-corner X) `1 by Th54;
( (S-min X) `2 = S-bound X & (SW-corner X) `1 <= (S-min X) `1 ) by Th54, EUCLID:52;
then S-min X in LSeg ((SW-corner X),(SE-corner X)) by A1, A4, GOBOARD7:8;
hence LSeg ((S-min X),(S-max X)) c= LSeg ((SW-corner X),(SE-corner X)) by A3, TOPREAL1:6; :: thesis: verum