Memory.slice_snoc: 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 216-222 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=216&end_line=222

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

# slice(ws, base, k + 1) is slice(ws, base, k) and word base + k.
def slice_snoc(+ws: List<&2, U32>, +base: Nat, +k: Nat, +h: {Nat.is_lt(Nat.add(base, k), SC.length(U32, ws)) == True{} : Bool}) -> {slice(ws, base, 1n+k) == SC.append(U32, slice(ws, base, k), Con{nthv(ws, Nat.add(base, k)), Nil{}}) : List<&2, U32>}:
  +ys = SC.drop(U32, ws, base)
  +hk = L.subst(Nat, z => {Nat.is_lt(k, z) == True{} : Bool}, Nat.sub(SC.length(U32, ws), base), SC.length(U32, ys), Equal.sym(Nat, SC.length(U32, ys), Nat.sub(SC.length(U32, ws), base), length_drop(ws, base)), lt_sub(base, k, SC.length(U32, ws), h))
  Equal.trans(List<&2, U32>, SC.take(U32, ys, 1n+k), SC.append(U32, SC.take(U32, ys, k), Con{nthv(ys, k), Nil{}}), SC.append(U32, SC.take(U32, ys, k), Con{nthv(ws, Nat.add(base, k)), Nil{}}),
    take_snoc(ys, k, hk),
    Equal.cong(U32, List<&2, U32>, z => SC.append(U32, SC.take(U32, ys, k), Con{z, Nil{}}), nthv(ys, k), nthv(ws, Nat.add(base, k)), nth_drop(ws, base, k)))

Uses (21):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.cong
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  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.add
  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=Nat.sub
  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=length_drop
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/argon2/memory.bend&name=lt_sub
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/argon2/memory.bend&name=nth_drop
  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/crypto/argon2/memory.bend&name=take_snoc
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/logic.bend&name=subst
  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
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend&name=take