reserve r, s, t, g for Real,

          r3, r1, r2, q3, p3 for Real;
reserve T for TopStruct,
  f for RealMap of T;
reserve p for Point of TOP-REAL 2,
  P for Subset of TOP-REAL 2,
  Z for non empty Subset of TOP-REAL 2,
  X for non empty compact Subset of TOP-REAL 2;

theorem
  LSeg(N-min X, N-max X) c= LSeg(NW-corner X, NE-corner X)
proof
A1: (NW-corner X)`2 = N-bound X & (NE-corner X)`2 = N-bound X by EUCLID:52;
A2: (N-max X)`1 <= (NE-corner X)`1 by Th38;
  (N-max X)`2 = N-bound X & (NW-corner X)`1 <= (N-max X)`1 by Th38,EUCLID:52;
  then
A3: N-max X in LSeg(NW-corner X, NE-corner X) by A1,A2,GOBOARD7:8;
A4: (N-min X)`1 <= (NE-corner X)`1 by Th38;
  (N-min X)`2 = N-bound X & (NW-corner X)`1 <= (N-min X)`1 by Th38,EUCLID:52;
  then N-min X in LSeg(NW-corner X, NE-corner X) by A1,A4,GOBOARD7:8;
  hence thesis by A3,TOPREAL1:6;
end;
