let C be non empty compact Subset of (TOP-REAL 2); :: thesis: W-min (L~ (SpStSeq C)) = SW-corner C
set X = L~ (SpStSeq C);
set S = W-most (L~ (SpStSeq C));
A1: W-most (L~ (SpStSeq C)) = LSeg ((SW-corner C),(NW-corner C)) by Th66;
A2: S-bound C <= N-bound C by Th22;
lower_bound (proj2 | (W-most (L~ (SpStSeq C)))) = lower_bound (rng (proj2 | (W-most (L~ (SpStSeq C))))) by RELSET_1:22
.= lower_bound (proj2 .: (W-most (L~ (SpStSeq C)))) by RELAT_1:115
.= lower_bound [.(S-bound C),(N-bound C).] by A1, Th70
.= S-bound C by A2, JORDAN5A:19 ;
hence W-min (L~ (SpStSeq C)) = SW-corner C by Th58; :: thesis: verum