reserve k,n,i,j for Nat;

theorem Th13:
  for K being Ring, n,m being Nat holds
  len (0.(K,n,m))=n & dom (0.(K,n,m))=Seg n
proof
  let K be Ring, n,m be Nat;
  len (n |-> (m |-> 0.K))=n by CARD_1:def 7;
  hence len (0.(K,n,m)) =n by MATRIX_3:def 1;
  hence thesis by FINSEQ_1:def 3;
end;
