ProofCore.wl_set: law of lawful-bytes@0.1.1.0
Import: import lawful-bytes@0.1.1.0/proof_core.bend as ProofCore
Lines 464-473 of lawful-bytes@0.1.1.0/proof_core.bend: https://jend.leeeet.dev/read.txt?path=lawful-bytes@0.1.1.0/proof_core.bend&start_line=464&end_line=473

import Base
import lawful-arrays@0.1.0.0/defs.bend as A
import lawful-arrays@0.1.0.0/proof_tree.bend as P
import lawful-arrays@0.1.0.0/proof_index.bend as I

# Writing word k (in range) sets the k-th of the word list.
law wl_set:
  for +t: P.Tree<U32>
  for +d: Nat
  for +k: U32
  for +w: U32
  for +hf: {A.full(U32, P.fromT(U32, t), d) == True{} : Bool}
  for +hd: {Nat.is_le(d, 29n) == True{} : Bool}
  for +hk: {Nat.is_lt(U32.to_nat(k), Nat.pow(2n, d)) == True{} : Bool}
  {WL(I.set_tree(U32, t, k, w)) == List.set(&2, U32, WL(t), U32.to_nat(k), w) : List<&2, U32>}

Uses (22):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Array.set
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  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.set
  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=Nat.is_lt
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.pow
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.to_nat
  https://jend.leeeet.dev/definition.txt?path=lawful-arrays@0.1.0.0/defs.bend&name=full
  https://jend.leeeet.dev/definition.txt?path=lawful-arrays@0.1.0.0/defs.bend&name=slot
  https://jend.leeeet.dev/definition.txt?path=lawful-arrays@0.1.0.0/defs.bend&name=view
  https://jend.leeeet.dev/definition.txt?path=lawful-arrays@0.1.0.0/proof_index.bend&name=set_tree
  https://jend.leeeet.dev/definition.txt?path=lawful-arrays@0.1.0.0/proof_index.bend&name=set_tree_eq
  https://jend.leeeet.dev/definition.txt?path=lawful-arrays@0.1.0.0/proof_index.bend&name=set_view_t
  https://jend.leeeet.dev/definition.txt?path=lawful-arrays@0.1.0.0/proof_index.bend&name=slot_small_t
  https://jend.leeeet.dev/definition.txt?path=lawful-arrays@0.1.0.0/proof_tree.bend&name=Tree
  https://jend.leeeet.dev/definition.txt?path=lawful-arrays@0.1.0.0/proof_tree.bend&name=fromT
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_core.bend&name=WL
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_core.bend&name=lt32