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;
