reserve i,j,k,l,m,n for Nat,
  D for non empty set,
  f for FinSequence of D;
reserve X for compact Subset of TOP-REAL 2;

theorem Th12:
  for p being Point of TOP-REAL 2 st p in X & p`1 = W-bound X
  holds p in W-most X
proof
  let p be Point of TOP-REAL 2 such that
A1: p in X and
A2: p`1 = W-bound X;
A3: (SW-corner X)`1 = W-bound X & (NW-corner X)`1 = W-bound X by EUCLID:52;
A4: (SW-corner X)`2 = S-bound X & (NW-corner X)`2 = N-bound X by EUCLID:52;
  S-bound X <= p`2 & p`2 <= N-bound X by A1,PSCOMP_1:24;
  then p in LSeg(SW-corner X, NW-corner X) by A2,A3,A4,GOBOARD7:7;
  hence thesis by A1,XBOOLE_0:def 4;
end;
