Listops.absdiff: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/listops.bend as Listops
Lines 138-148 of bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/listops.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/listops.bend&start_line=138&end_line=148

import Base

# (x - y) + (y - x) == 0 exactly when x == y
def absdiff(x: Nat, y: Nat) -> {Nat.is_eq(Nat.add(Nat.sub(x, y), Nat.sub(y, x)), 0n) == Nat.is_eq(x, y) : Bool}:
  match x y:
    case 0n 0n:
      {==}
    case 0n 1n+q:
      {==}
    case 1n+p 0n:
      {==}
    case 1n+p 1n+q:
      absdiff(p, q)

Uses (5):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.add
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_eq
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.sub