reserve n for Nat,
  i,j for Nat,
  r,s,r1,s1,r2,s2,r9,s9 for Real,
  p,q for Point of TOP-REAL 2,
  G for Go-board,
  x,y for set,
  v for Point of Euclid 2;

theorem
  1 <= i & i+1 <= len G implies LSeg(1/2*(G*(i,1)+G*(i+1,1))-|[0,1]|,p)
  meets Int cell(G,i,0)
proof
  assume
A1: 1 <= i & i+1 <= len G;
  now
    take a = 1/2*(G*(i,1)+G*(i+1,1))-|[0,1]|;
    thus a in LSeg(1/2*(G*(i,1)+G*(i+1,1))-|[0,1]|,p) by RLTOPSP1:68;
    thus a in Int cell(G,i,0) by A1,Th33;
  end;
  hence thesis by XBOOLE_0:3;
end;
