let C be non empty compact Subset of (TOP-REAL 2); :: thesis: E-min (L~ (SpStSeq C)) = SE-corner C
set X = L~ (SpStSeq C);
set S = E-most (L~ (SpStSeq C));
A1: E-most (L~ (SpStSeq C)) = LSeg (SE-corner C),(NE-corner C) by Th77;
A2: S-bound C <= N-bound C by Th24;
inf (proj2 | (E-most (L~ (SpStSeq C)))) = inf (rng (proj2 | (E-most (L~ (SpStSeq C))))) by FUNCT_2:45
.= inf (proj2 .: (E-most (L~ (SpStSeq C)))) by RELAT_1:148
.= inf [.(S-bound C),(N-bound C).] by A1, Th80
.= S-bound C by A2, JORDAN5A:20 ;
hence E-min (L~ (SpStSeq C)) = SE-corner C by Th69; :: thesis: verum