@add nat (@has_add.mk nat nat.add) a b
@add nat (@has_add.mk nat nat.add) (@mul nat (@has_mul.mk nat nat.mul) (@add nat (@has_add.mk nat nat.add) a b) c)
  (@one nat (@has_one.mk nat (succ zero)))
@add int (@has_add.mk int int.add) (@add int (@has_add.mk int int.add) (of_nat a) i)
  (@bit1 int (@has_one.mk int (@one int (@has_one.mk int (of_nat (@one nat (@has_one.mk nat (succ zero)))))))
     (@has_add.mk int int.add)
     (@bit1 int (@has_one.mk int (@one int (@has_one.mk int (of_nat (@one nat (@has_one.mk nat (succ zero)))))))
        (@has_add.mk int int.add)
        (@bit1 int (@has_one.mk int (@one int (@has_one.mk int (of_nat (@one nat (@has_one.mk nat (succ zero)))))))
           (@has_add.mk int int.add)
           (@one int
              (@has_one.mk int (@one int (@has_one.mk int (of_nat (@one nat (@has_one.mk nat (succ zero)))))))))))
@add A (@has_add.mk A (@ring.add A s)) x (@mul A (@has_mul.mk A (@ring.mul A s)) y x)
@add A (@has_add.mk A (@ring.add A s)) x
  (@bit1 A (@has_one.mk A (@ring.one A s)) (@has_add.mk A (@ring.add A s)) (@one A (@has_one.mk A (@ring.one A s))))