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 & 1 <= j & j+1 <= width G implies LSeg(1/2*(G*(i
  ,j)+G*(i+1,j+1)),p) meets Int cell(G,i,j)
proof
  assume
A1: 1 <= i & i+1 <= len G & 1 <= j & j+1 <= width G;
  now
    take a = 1/2*(G*(i,j)+G*(i+1,j+1));
    thus a in LSeg(1/2*(G*(i,j)+G*(i+1,j+1)),p) by RLTOPSP1:68;
    thus a in Int cell(G,i,j) by A1,Th31;
  end;
  hence thesis by XBOOLE_0:3;
end;
