reserve i,j,k,x for object;

theorem Th3:
  for A,B being non empty set, N,M being ManySortedSet of [:A,B:]
st for i being Element of A, j being Element of B holds N.(i,j) = M.(i,j) holds
  M = N
proof
  let A,B be non empty set, N,M be ManySortedSet of [:A,B:];
  assume
  for i being Element of A, j being Element of B holds N.(i,j) = M.(i, j);
  then for i,j st i in A & j in B holds N.(i,j) = M.(i,j);
  hence thesis by Th2;
end;
