ProofFastAppend.fin_eq: law of lawful-bytes@0.1.1.0
Import: import lawful-bytes@0.1.1.0/proof_fast_append.bend as ProofFastAppend
Lines 1246-1262 of lawful-bytes@0.1.1.0/proof_fast_append.bend: https://jend.leeeet.dev/read.txt?path=lawful-bytes@0.1.1.0/proof_fast_append.bend&start_line=1246&end_line=1262

import Base
import lawful-bytes@0.1.1.0/defs.bend as D

# The last list step: the bytes of the prefix and of the words make the slice.
law fin_eq:
  for +v1: List<&2, U32>
  for +vd: List<&2, U32>
  for +us: List<&2, U32>
  for +ls: Nat
  for +s: Nat
  for +hh: Nat
  for +qn: Nat
  for +np: Nat
  for +nn: Nat
  for +hv: {v1 == List.append(&2, U32, vd, D.slice(List.take(&2, U32, us, ls), s, hh)) : List<&2, U32>}
  for +hq: {qn == Nat.add(s, hh) : Nat}
  for +hnp: {np == Nat.sub(nn, hh) : Nat}
  for +hhn: {Nat.is_le(hh, nn) == True{} : Bool}
  for +hb: {Nat.is_le(Nat.add(s, nn), ls) == True{} : Bool}
  {List.append(&2, U32, v1, List.take(&2, U32, List.drop(&2, U32, us, qn), np)) == List.append(&2, U32, vd, D.slice(List.take(&2, U32, us, ls), s, nn)) : List<&2, U32>}

Uses (20):
  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=List.append
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List.drop
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List.take
  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_le
  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=lawful-arrays@0.1.0.0/proof_base.bend&name=subst
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/defs.bend&name=slice
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_append.bend&name=append_assoc
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_fast_append.bend&name=slice_split
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_fast_append.bend&name=slice_take
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=add_assoc
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=le_sub_add