reserve m,k,j,j1,i,i1,i2,n for Nat,
  r,s for Real,
  C for compact non vertical non horizontal Subset of TOP-REAL 2,
  G for Go-board,
  p for Point of TOP-REAL 2;

theorem
  for f being non constant standard special_circular_sequence st
  LeftComp f = UBD L~f holds f is clockwise_oriented
proof
  let f be non constant standard special_circular_sequence such that
A1: LeftComp f = UBD L~f;
  set g = Rotate(f,N-min L~f);
  assume not thesis;
  then g is not clockwise_oriented by Th40;
  then
A2: Rev g is clockwise_oriented by REVROT_1:38;
  L~f = L~g by REVROT_1:33;
  then UBD L~f = UBD L~Rev g by SPPOL_2:22
    .= LeftComp Rev g by A2,GOBRD14:36
    .= RightComp g by GOBOARD9:23
    .= RightComp f by REVROT_1:37;
  hence contradiction by A1,SPRECT_4:6;
end;
