reserve i, i1, i2, j, j1, j2, k, m, n, t for Nat,
  D for non empty Subset of TOP-REAL 2,
  E for compact non vertical non horizontal Subset of TOP-REAL 2,
  C for compact connected non vertical non horizontal Subset of TOP-REAL 2,
  G for Go-board,
  p, q, x for Point of TOP-REAL 2,
  r, s for Real;

theorem Th35:
  m <= n & 1 < i & i+1 < width Gauge(D,m) implies 1 < 2|^(n-'m)*(i
  -1)+2 & 2|^(n-'m)*(i-1)+2 <= width Gauge(D,n)
proof
  len Gauge(D,n) = width Gauge(D,n) & len Gauge(D,m) = width Gauge(D,m) by
JORDAN8:def 1;
  hence thesis by Th34;
end;
