ProofIndex.get_set_other_t: law of lawful-arrays@0.1.0.0
Import: import lawful-arrays@0.1.0.0/proof_index.bend as ProofIndex
Lines 626-637 of lawful-arrays@0.1.0.0/proof_index.bend: https://jend.leeeet.dev/read.txt?path=lawful-arrays@0.1.0.0/proof_index.bend&start_line=626&end_line=637

import Base
import lawful-arrays@0.1.0.0/defs.bend as D
import lawful-arrays@0.1.0.0/proof_tree.bend as P

law get_set_other_t:
  for -T: Data
  for +t: P.Tree<T>
  for +d: Nat
  for +i: U32
  for +j: U32
  for +v: T
  for +hf: {D.full(T, P.fromT(T, t), d) == True{} : Bool}
  for +hd: {Nat.is_lt(d, 32n) == True{} : Bool}
  for +hij: {Nat.is_eq(D.slot(i, d), D.slot(j, d)) == False{} : Bool}
  {Pair.snd(Array<T>, T, Array.get(T, Array.set(T, P.fromT(T, t), i, v), j))
    == Pair.snd(Array<T>, T, Array.get(T, P.fromT(T, t), j)) : T}

Uses (29):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Array
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Array.get
  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.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.get
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List.set
  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.is_eq
  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=Pair.snd
  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/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_base.bend&name=get_set_ne
  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-arrays@0.1.0.0/proof_index.bend&name=get_view_t
  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=unsome
  https://jend.leeeet.dev/definition.txt?path=lawful-arrays@0.1.0.0/proof_shape.bend&name=set_full
  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