Array.get_set_other: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/lib/array.bend as Array
Lines 342-347 of bend-collections-laws-crypto@1.0.0.0/proofs/lib/array.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/array.bend&start_line=342&end_line=347

import Base
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/logic.bend as L
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/list.bend as LL
import bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend as SC

def get_set_other(-T: Data, +d: Nat, +t: Tree<T>, +i: U32, +j: U32, +v: T, +x: T, +y: T, +hd: {Nat.is_lt(d, 32n) == True{} : Bool}, +hi: {Nat.is_lt(U32.to_nat(i), SC.pow2(d)) == True{} : Bool}, +hj: {Nat.is_lt(U32.to_nat(j), SC.pow2(d)) == True{} : Bool}, +ne: {Nat.is_eq(U32.to_nat(i), U32.to_nat(j)) == False{} : Bool}, +hx: {SC.nth(T, slots(T, t), U32.to_nat(i)) == Some{x} : Maybe<&2, T>}, +hy: {SC.nth(T, slots(T, t), U32.to_nat(j)) == Some{y} : Maybe<&2, T>}, +pf: {perfect(T, d, t) == True{} : Bool}) -> {Array.get(T, Array.set(T, thaw(T, t), i, v), j) == (thaw(T, upd(T, d, t, U32.to_nat(i), v)), y) : Array<T> & T}:
  +t2 = upd(T, d, t, U32.to_nat(i), v)
  %Equal.sym(Array<T>, Array.set(T, thaw(T, t), i, v), thaw(T, t2), set(T, d, t, i, v, x, hd, hi, hx, pf)) : {Array.get(T, _, j) == (thaw(T, t2), y) : Array<T> & T}
  get(T, d, t2, j, y, hd, hj,
    L.subst(List<&2, T>, ys => {SC.nth(T, ys, U32.to_nat(j)) == Some{y} : Maybe<&2, T>}, SC.update(T, slots(T, t), U32.to_nat(i), v), slots(T, t2), Equal.sym(List<&2, T>, slots(T, t2), SC.update(T, slots(T, t), U32.to_nat(i), v), upd_slots(T, d, t, U32.to_nat(i), v, hi, pf)), Equal.trans(Maybe<&2, T>, SC.nth(T, SC.update(T, slots(T, t), U32.to_nat(i), v), U32.to_nat(j)), SC.nth(T, slots(T, t), U32.to_nat(j)), Some{y}, LL.nth_update_other(T, slots(T, t), U32.to_nat(i), U32.to_nat(j), v, ne), hy)),
    upd_perfect(T, d, t, U32.to_nat(i), v, pf))

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.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=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
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Sigma
  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=bend-collections-laws-crypto@1.0.0.0/proofs/lib/array.bend&name=Tree
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/array.bend&name=get
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/array.bend&name=perfect
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/array.bend&name=set
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/array.bend&name=slots
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/array.bend&name=thaw
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/array.bend&name=upd
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/array.bend&name=upd_perfect
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/array.bend&name=upd_slots
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/list.bend&name=nth_update_other
  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=nth
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend&name=pow2
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend&name=update