reserve i,i1,i2,i9,i19,j,j1,j2,j9,j19,k,l,m,n for Nat;
reserve r,s,r9,s9 for Real;
reserve D for set,
  f for FinSequence of D,
  G for Matrix of D;
reserve G for Go-board,
  p for Point of TOP-REAL 2;
reserve T for non empty Subset of TOP-REAL 2;

theorem Th10:
  for n being Nat holds len Gauge(T,n) >= 4
proof
  let n be Nat;
  set G = Gauge(T,n);
A1: len G = 2|^n + 3 by Def1;
  2|^n >= n + 1 by NEWTON:85;
  then
A2: len G >= n + 1 + 3 by A1,XREAL_1:6;
  n+4 >= 4 by NAT_1:12;
  hence thesis by A2,XXREAL_0:2;
end;
