Definition is_upper_triangular_pred :
  forall (F : field) (m n : Nat), Predicate (Mmn F m n).Definition is_lower_triangular_pred :
  forall (F : field) (m n : Nat), Predicate (Mmn F m n).Definition is_diagonal_pred :
  forall (F : field) (n : Nat), Predicate (Mmn F n n).

Lemma lo_triang_subspace : forall (F : field) (m n : Nat), is_subspace (is_lower_triangular_pred F m n).