theorem
  for p being Point of TOP-REAL 2 st f/.1 = N-min L~f & p`2 < S-bound (
  L~f) holds p in LeftComp f
proof
  let p be Point of TOP-REAL 2;
  assume that
A1: f/.1 = N-min L~f and
A2: p`2< S-bound(L~f);
  set g=SpStSeq L~f;
A3: LeftComp g c= LeftComp f by A1,SPRECT_3:41;
  S-bound L~ g=S-bound L~f by SPRECT_1:59;
  then p in LeftComp g by A2,SPRECT_3:40;
  hence thesis by A3;
end;
