reserve p,q for Point of TOP-REAL 2,
  i,i1,i2,j,j1,j2,k for Nat,
  r,s for Real,
  G for Matrix of TOP-REAL 2;
reserve f for standard special_circular_sequence;

theorem Th21:
  for G being Go-board holds j < width G & 1 <= i & i < len G
  implies LSeg(G*(i,j+1),G*(i+1,j+1)) c= cell(G,i,j)
proof
  let G be Go-board;
  assume that
A1: j < width G and
A2: 1 <= i and
A3: i < len G;
A4: LSeg(G*(i,j+1),G*(i+1,j+1)) c= h_strip(G,j) by A1,A2,A3,Th15;
A5: 1 <= j+1 by NAT_1:11;
A6: i+1 <= len G by A3,NAT_1:13;
  j+1 <= width G by A1,NAT_1:13;
  then LSeg(G*(i,j+1),G*(i+1,j+1)) c= v_strip(G,i) by A2,A5,A6,Th20;
  hence thesis by A4,XBOOLE_1:19;
end;
