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 Th69;
A2: S-bound C <= N-bound C by Th22;
lower_bound (proj2 | (E-most (L~ (SpStSeq C)))) = lower_bound (rng (proj2 | (E-most (L~ (SpStSeq C))))) by RELSET_1:22
.= lower_bound (proj2 .: (E-most (L~ (SpStSeq C)))) by RELAT_1:115
.= lower_bound [.(S-bound C),(N-bound C).] by A1, Th72
.= S-bound C by A2, JORDAN5A:19 ;
hence E-min (L~ (SpStSeq C)) = SE-corner C by Th61; :: thesis: verum