theorem Th80:
  S-min L~SpStSeq C = SW-corner C
proof
  set X = L~SpStSeq C, S = S-most X;
A1: S = LSeg(SW-corner C,SE-corner C) by Th68;
A2: W-bound C <= E-bound C by Th21;
  lower_bound (proj1|S) = lower_bound rng(proj1|S) by RELSET_1:22
    .= lower_bound(proj1.:S) by RELAT_1:115
    .= lower_bound [.W-bound C,E-bound C.] by A1,Th73
    .= W-bound C by A2,JORDAN5A:19;
  hence thesis by Th59;
end;
