Peano numbers type-level implementation works with classes but not traits

Question

The following type level implementation of subtraction on Peano numbers using match types works

sealed trait Nat
class O extends Nat
class S[N <: Nat] extends Nat

type _1 = S[O]
type _2 = S[_1]
type _3 = S[_2]

type minus[a <: Nat, b <: Nat] = (a, b) match
  case (O, _) => O
  case (S[n], O) => a
  case (S[n], S[m]) => n minus m

type x = _2 minus _1
summon[x =:= _1]
// val res0: S[O] =:= S[O] = generalized constraint

however if classes are changed to traits

trait O extends Nat
trait S[N <: Nat] extends Nat

then why does it not work

scala> type x = _2 minus _1
// defined alias type x = minus[_2, _1]

scala> summon[x =:= _1]
1 |summon[x =:= _1]
  |                ^
  |                Cannot prove that x =:= _1.