reserve m,n,i,i2,j for Nat,
  r,r1,r2,s,t for Real,
  x,y,z for object;
reserve p,p1,p2,p3,q,q1,q2,q3,q4 for Point of TOP-REAL n;
reserve u for Point of Euclid n;
reserve R for Subset of TOP-REAL n;
reserve P,Q for Subset of TOP-REAL n;
reserve D for non vertical non horizontal non empty compact Subset of TOP-REAL
  2;
reserve f for clockwise_oriented non constant standard
  special_circular_sequence;

theorem
  for p being Point of TOP-REAL 2 st f/.1 = N-min L~f & p`2 > N-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>N-bound(L~f);
  set g=SpStSeq L~f;
A3: LeftComp g c= LeftComp f by A1,SPRECT_3:41;
  N-bound L~ g=N-bound L~f by SPRECT_1:60;
  then p in LeftComp g by A2,SPRECT_3:40;
  hence thesis by A3;
end;
