reserve i, i1, i2, j, j1, j2, k, m, n, t for Nat,
  D for non empty Subset of TOP-REAL 2,
  E for compact non vertical non horizontal Subset of TOP-REAL 2,
  C for compact connected non vertical non horizontal Subset of TOP-REAL 2,
  G for Go-board,
  p, q, x for Point of TOP-REAL 2,
  r, s for Real;

theorem Th5:
  p in S-most D implies p`2 = S-bound D
proof
  assume p in S-most D;
  then
A1: p in LSeg(SW-corner D, SE-corner D) by XBOOLE_0:def 4;
  (SE-corner D)`2 = S-bound D by EUCLID:52
    .= (SW-corner D)`2 by EUCLID:52;
  hence p`2 = (SW-corner D)`2 by A1,GOBOARD7:6
    .= S-bound D by EUCLID:52;
end;
