(** Similarly, to state that two numbers [n] and [m] are equal, we can say either (1) that [beq_nat n m] returns [true] or (2) that [n = m].  These two notions are equivalent. *)

Theorem beq_nat_true_iff : forall n1 n2 : nat,
beq_nat n1 n2 = true <-> n1 = n2.