let C be non empty compact Subset of (TOP-REAL 2); :: thesis: N-max (L~ (SpStSeq C)) = NE-corner C
set X = L~ (SpStSeq C);
set S = N-most (L~ (SpStSeq C));
A1: N-most (L~ (SpStSeq C)) = LSeg (NW-corner C),(NE-corner C) by Th75;
A2: W-bound C <= E-bound C by Th23;
sup (proj1 | (N-most (L~ (SpStSeq C)))) = sup (rng (proj1 | (N-most (L~ (SpStSeq C))))) by FUNCT_2:45
.= sup (proj1 .: (N-most (L~ (SpStSeq C)))) by RELAT_1:148
.= sup [.(W-bound C),(E-bound C).] by A1, Th79
.= E-bound C by A2, JORDAN5A:20 ;
hence N-max (L~ (SpStSeq C)) = NE-corner C by Th68; :: thesis: verum