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 Th19:
  for G being Y_equal-in-column Y_increasing-in-line non
  empty-yielding Matrix of TOP-REAL 2 holds width G = card(proj2.:Values G)
proof
  let G be Y_equal-in-column Y_increasing-in-line non empty-yielding Matrix of
  TOP-REAL 2;
  width G <= card(proj2.:Values G) & card(proj2.:Values G) <= width G by Th17
,Th18;
  hence thesis by XXREAL_0:1;
end;
