theorem Th16:
  for G being X_equal-in-line X_increasing-in-column non
  empty-yielding Matrix of TOP-REAL 2 holds len G = card(proj1.:Values G)
proof
  let G be X_equal-in-line X_increasing-in-column non empty-yielding Matrix of
  TOP-REAL 2;
  len G <= card(proj1.:Values G) & card(proj1.:Values G) <= len G by Th14,Th15;
  hence thesis by XXREAL_0:1;
end;
