Memory.drop_append_le: 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 365-374 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=365&end_line=374

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/logic.bend as L

def drop_append_le(+xs: List<&2, U32>, +ys: List<&2, U32>, +n: Nat, +h: {Nat.is_le(n, SC.length(U32, xs)) == True{} : Bool}) -> {SC.drop(U32, SC.append(U32, xs, ys), n) == SC.append(U32, SC.drop(U32, xs, n), ys) : List<&2, U32>}:
  match xs n:
    case Nil{} 0n:
      Equal.trans(List<&2, U32>, SC.drop(U32, ys, 0n), ys, SC.append(U32, SC.drop(U32, Nil{}, 0n), ys), drop_zero(ys), {==})
    case Nil{} 1n+p:
      Empty.absurd({SC.drop(U32, ys, 1n+p) == SC.append(U32, SC.drop(U32, Nil{}, 1n+p), ys) : List<&2, U32>}, L.false_true(h))
    case Con{x, t} 0n:
      {==}
    case Con{x, +t} 1n+ +p:
      drop_append_le(t, ys, p, h)

Uses (12):
  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.trans
  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_le
  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=drop_zero
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/logic.bend&name=false_true
  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=drop
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend&name=length