Nat.even_odd: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend as Nat
Lines 351-358 of bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend&start_line=351&end_line=358

import Base

def even_odd(+a: Nat, +b: Nat, e: {Nat.double(a) == 1n+Nat.double(b) : Nat}) -> Empty:
  match a b:
    case 0n _:
      zero_succ(Nat.double(b), e)
    case 1n+p 0n:
      succ_zero(Nat.double(p), succ_inj(1n+Nat.double(p), 0n, e))
    case 1n+p 1n+q:
      even_odd(p, q, succ_inj(Nat.double(p), 1n+Nat.double(q), succ_inj(1n+Nat.double(p), 2n+Nat.double(q), e)))

Uses (6):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Empty
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.double
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend&name=succ_inj
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend&name=succ_zero
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend&name=zero_succ