Memory.take_upd: 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 514-521 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=514&end_line=521

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 take_upd(+V: List<&2, U32>, +i: Nat, +w: U32, +h: {Nat.is_lt(i, SC.length(U32, V)) == True{} : Bool}) -> {SC.take(U32, SC.update(U32, V, i, w), 1n+i) == SC.append(U32, SC.take(U32, V, i), Con{w, Nil{}}) : List<&2, U32>}:
  match V i:
    case Nil{} _:
      Empty.absurd({SC.take(U32, SC.update(U32, Nil{}, i, w), 1n+i) == SC.append(U32, SC.take(U32, Nil{}, i), Con{w, Nil{}}) : List<&2, U32>}, N.lt_zero_absurd(i, h))
    case Con{x, +r} 0n:
      Equal.cong(List<&2, U32>, List<&2, U32>, z => Con{w, z}, SC.take(U32, r, 0n), Nil{}, LL.sc_take_zero(U32, r))
    case Con{+x, +r} 1n+ +j:
      Equal.cong(List<&2, U32>, List<&2, U32>, z => Con{x, z}, SC.take(U32, SC.update(U32, r, j, w), 1n+j), SC.append(U32, SC.take(U32, r, j), Con{w, Nil{}}), take_upd(r, j, w, 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/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=append
  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
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend&name=update