reserve S for Subset of TOP-REAL 2,
  C,C1,C2 for non empty compact Subset of TOP-REAL 2,
  p,q for Point of TOP-REAL 2;
reserve i,j,k for Nat,
  t,r1,r2,s1,s2 for Real;
reserve D1 for non vertical non empty compact Subset of TOP-REAL 2,
  D2 for non horizontal non empty compact Subset of TOP-REAL 2,
  D for non vertical non horizontal non empty compact Subset of TOP-REAL 2;

theorem Th74:
  W-min L~SpStSeq C = SW-corner C
proof
  set X = L~SpStSeq C, S = W-most X;
A1: S = LSeg(SW-corner C,NW-corner C) by Th66;
A2: S-bound C <= N-bound C by Th22;
  lower_bound (proj2|S) = lower_bound rng(proj2|S) by RELSET_1:22
    .= lower_bound(proj2.:S) by RELAT_1:115
    .= lower_bound [.S-bound C,N-bound C.] by A1,Th70
    .= S-bound C by A2,JORDAN5A:19;
  hence thesis by Th58;
end;
