Memory.slice_one: 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 224-231 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=224&end_line=231

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/list.bend as LL
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend as N

def slice_one(+ws: List<&2, U32>, +base: Nat, +h: {Nat.is_lt(base, SC.length(U32, ws)) == True{} : Bool}) -> {slice(ws, base, 1n) == Con{nthv(ws, base), Nil{}} : List<&2, U32>}:
  match ws base:
    case Nil{} _:
      Empty.absurd({slice(Nil{}, base, 1n) == Con{nthv(Nil{}, base), Nil{}} : List<&2, U32>}, N.lt_zero_absurd(base, h))
    case Con{+x, +t} 0n:
      Equal.cong(List<&2, U32>, List<&2, U32>, z => Con{x, z}, SC.take(U32, t, 0n), Nil{}, LL.sc_take_zero(U32, t))
    case Con{x, +t} 1n+ +b:
      slice_one(t, b, h)

Uses (13):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  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=Nat.is_lt
  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/crypto/argon2/memory.bend&name=nthv
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/argon2/memory.bend&name=slice
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/list.bend&name=sc_take_zero
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend&name=lt_zero_absurd
  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