ProofShift.ns.odd_even: def of bend-osdev-word64@0.1.1.0
Import: import bend-osdev-word64@0.1.1.0/proof_shift.bend as ProofShift
Lines 116-124 of bend-osdev-word64@0.1.1.0/proof_shift.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-word64@0.1.1.0/proof_shift.bend&start_line=116&end_line=124

import Base

# 1 + 2a = 2b never holds; 2a = 2b gives a = b
def ns.odd_even(a: Nat, b: Nat, e: {1n+Nat.double(a) == Nat.double(b) : Nat}) -> Empty:
  match a b:
    case _ 0n:
      ns.sz(Nat.double(a), e)
    case 0n 1n+ +q:
      ns.sz(Nat.double(q), Equal.sym(Nat, 0n, 1n+Nat.double(q), ns.succ_inj(0n, 1n+Nat.double(q), e)))
    case 1n+ +p 1n+ +q:
      ns.odd_even(p, q, ns.succ_inj(1n+Nat.double(p), Nat.double(q), ns.succ_inj(2n+Nat.double(p), 1n+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=Equal.sym
  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-osdev-word64@0.1.1.0/proof_shift.bend&name=ns.succ_inj
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-word64@0.1.1.0/proof_shift.bend&name=ns.sz