a + of_num b = 10 : Prop
@eq.{1} nat
  (@add.{1} nat nat._trans_of_decidable_linear_ordered_semiring_2 ((λ (x : nat), x) a)
     (nat.of_num (@bit0.{1} num num_has_add (@one.{1} num num_has_one))))
  (@bit0.{1} nat nat._trans_of_decidable_linear_ordered_semiring_2
     (@bit1.{1} nat nat._trans_of_decidable_linear_ordered_semiring_22 nat._trans_of_decidable_linear_ordered_semiring_2
        (@bit0.{1} nat nat._trans_of_decidable_linear_ordered_semiring_2
           (@one.{1} nat nat._trans_of_decidable_linear_ordered_semiring_22)))) :
  Prop