reserve i, j, n for Nat,
  f for non constant standard special_circular_sequence,
  g for clockwise_oriented non constant standard special_circular_sequence,
  p, q for Point of TOP-REAL 2,
  P for Subset of TOP-REAL 2,
  C for compact non vertical non horizontal Subset of TOP-REAL 2,
  G for Go-board;

theorem
  1 <= i & i < len G & 1 <= j & j < width G implies cell(G,i,j) is compact
proof
  assume 1 <= i & i < len G & 1 <= j & j < width G;
  then
  cell(G,i,j) = product ((1,2) --> ([.G*(i,1)`1,G*(i+1,1)`1.], [.G*(1,j)`2
  ,G*(1,j+1)`2.])) by Th3;
  hence thesis by TOPREAL6:78;
end;
