reserve i,j,k,n for Nat,
  X,Y,a,b,c,x for set,
  r,s for Real;
reserve f,g for FinSequence of TOP-REAL 2;
reserve f for non constant standard special_circular_sequence,
  p,p1,p2,q for Point of TOP-REAL 2;
reserve G for Go-board;

theorem Th21:
  for f,k st 1<=k & k+1<=len f holds left_cell(f,k) is convex
proof
  let f,k;
  assume 1<=k & k+1<=len f;
  then ex i,j st i <= len GoB f & j <= width GoB f & cell(GoB f,i,j) =
  left_cell(f,k) by GOBOARD9:11;
  hence thesis by Th20;
end;
