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 Th70:
  proj2.:LSeg(SW-corner C,NW-corner C) = [.S-bound C,N-bound C.]
proof
A1: (NW-corner C)`2 = N-bound C by EUCLID:52;
  (SW-corner C)`2 = S-bound C by EUCLID:52;
  hence thesis by A1,Th22,Th53;
end;
