reserve i,j,k,n,m for Nat;
reserve p,q for Point of TOP-REAL 2;
reserve G for Go-board;
reserve C for Subset of TOP-REAL 2;

theorem
  for f being clockwise_oriented non constant standard
  special_circular_sequence st f/.1 = N-min L~f holds LSeg(f/.1,f/.2) c= L~
  SpStSeq L~f
proof
  let f be clockwise_oriented non constant standard special_circular_sequence;
A1: N-most L~f c= LSeg(NW-corner L~f,NE-corner L~f) by XBOOLE_1:17;
  assume
A2: f/.1 = N-min L~f;
  then
A3: f/.2 in N-most L~f by SPRECT_2:30;
A4: LSeg(NW-corner L~f,NE-corner L~f) c= L~SpStSeq L~f by Th14;
  f/.1 in LSeg(NW-corner L~f,NE-corner L~f) by A2,Th15;
  then LSeg(f/.1,f/.2) c= LSeg(NW-corner L~f,NE-corner L~f) by A3,A1,TOPREAL1:6
;
  hence thesis by A4;
end;
