Memory.take_all: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/argon2/memory.bend as Memory
Lines 56-63 of bend-collections-laws-crypto@1.0.0.0/proofs/crypto/argon2/memory.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/argon2/memory.bend&start_line=56&end_line=63

import Base
import bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend as SC
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend as N

def take_all(+xs: List<&2, U32>, +n: Nat, +h: {SC.length(U32, xs) == n : Nat}) -> {SC.take(U32, xs, n) == xs : List<&2, U32>}:
  match xs n:
    case Nil{} _:
      {==}
    case Con{h1, t} 0n:
      Empty.absurd({SC.take(U32, Con{h1, t}, 0n) == Con{h1, t} : List<&2, U32>}, N.succ_zero(SC.length(U32, t), h))
    case Con{+h1, +t} 1n+ +p:
      Equal.cong(List<&2, U32>, List<&2, U32>, z => Con{h1, z}, SC.take(U32, t, p), t, take_all(t, p, N.succ_inj(SC.length(U32, t), p, h)))

Uses (9):
  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.cong
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  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/spec/lib/common.bend&name=length
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend&name=take