(* Some alternative names: *)
Notation mul_eq_0_l := eq_mul_0_l.
Notation mul_eq_0_r := eq_mul_0_r.

(* The converse theorems require nonnegativity (or nonpositivity) of the other variable *)
Theorem square_lt_simpl_nonneg : forall n m, 0 <= m -> n * n < m * m -> n < m.