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 Th49:
  2 < X-SpanStart(C,n) & X-SpanStart(C,n) < len Gauge(C,n)
proof
  2|^(n-'1) > 0 by NEWTON:83;
  then 2|^(n-'1) + 2 > 0 qua Nat+2 by XREAL_1:6;
  hence 2 < X-SpanStart(C,n);
  n-'1 <= n by NAT_D:44;
  then len Gauge(C,n) = 2|^n + 3 & 2|^(n-'1) <= 2|^n by JORDAN8:def 1
,PREPOWER:93;
  hence thesis by XREAL_1:8;
end;
