# Adding zero changes nothing: one proof, published to test the hub
import Base

law add_zero:
  for x: Nat
  {Nat.add(x, 0n) == x : Nat}

def add_zero(x):
  match x:
    case 0n:
      {==}
    case 1n+p:
      %add_zero(p) : {1n+Nat.add(p, 0n) == 1n+_ : Nat}
      {==}