ProofSame.lists_step: law of lawful-bytes@0.1.1.0
Import: import lawful-bytes@0.1.1.0/proof_same.bend as ProofSame
Lines 425-443 of lawful-bytes@0.1.1.0/proof_same.bend: https://jend.leeeet.dev/read.txt?path=lawful-bytes@0.1.1.0/proof_same.bend&start_line=425&end_line=443

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

# One step of a comparison loop: the two slices from x and y, with the
# accumulated test rebracketed.
law lists_step:
  for +acc: Bool
  for +xs: List<&2, U32>
  for +ys: List<&2, U32>
  for +i: Nat
  for +j: Nat
  for +i1: U32
  for +j1: U32
  for +k: Nat
  for +x: U32
  for +y: U32
  for +hx: {List.get(&2, U32, xs, i) == Some{x} : Maybe<&2, U32>}
  for +hy: {List.get(&2, U32, ys, j) == Some{y} : Maybe<&2, U32>}
  for +ei: {U32.to_nat(i1) == Nat.add(i, 1n) : Nat}
  for +ej: {U32.to_nat(j1) == Nat.add(j, 1n) : Nat}
  {Bool.and(Bool.and(acc, U32.is_eq(x, y)), D.list_eq(D.slice(xs, U32.to_nat(i1), k), D.slice(ys, U32.to_nat(j1), k)))
    == Bool.and(acc, D.list_eq(D.slice(xs, i, 1n+k), D.slice(ys, j, 1n+k))) : Bool}

Uses (15):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool.and
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List.get
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Maybe
  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=U32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.is_eq
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.to_nat
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/defs.bend&name=list_eq
  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_same.bend&name=and_assoc
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_same.bend&name=slice_cons