ProofShift.ns.double_inj: def of bend-osdev-word64@0.1.1.0
Import: import bend-osdev-word64@0.1.1.0/proof_shift.bend as ProofShift
Lines 126-135 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=126&end_line=135

import Base
import bend-osdev-word64@0.1.1.0/proof_value.bend as P

def ns.double_inj(a: Nat, b: Nat, e: {Nat.double(a) == Nat.double(b) : Nat}) -> {a == b : Nat}:
  match a b:
    case 0n 0n:
      {==}
    case 0n 1n+ +q:
      Empty.absurd({0n == 1n+q : Nat}, ns.sz(1n+Nat.double(q), Equal.sym(Nat, 0n, 2n+Nat.double(q), e)))
    case 1n+ +p 0n:
      Empty.absurd({1n+p == 0n : Nat}, ns.sz(1n+Nat.double(p), e))
    case 1n+ +p 1n+ +q:
      P.wn.succ_cong(p, q, ns.double_inj(p, q, ns.succ_inj(Nat.double(p), Nat.double(q), ns.succ_inj(1n+Nat.double(p), 1n+Nat.double(q), e))))

Uses (7):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Empty.absurd
  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
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-word64@0.1.1.0/proof_value.bend&name=wn.succ_cong