Array.tupd_perfect: 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 170-181 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=170&end_line=181

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/spec/lib/common.bend as SC

def tupd_perfect(-T: Data, +d: Nat, +t: Tree<T>, +j: Nat, +v: T, +b: Bool, +pf: {perfect(T, d, t) == True{} : Bool}) -> {perfect(T, d, tupd(T, d, t, j, v, b)) == True{} : Bool}:
  match d t b:
    case 0n TLeaf{x} _:
      {==}
    case 0n TNode{l, r} _:
      pf
    case 1n+p TLeaf{x} _:
      pf
    case 1n+ +p TNode{+l, +r} True{}:
      L.and_intro(perfect(T, p, tupd(T, p, l, j, v, ndec(p, j))), perfect(T, p, r), tupd_perfect(T, p, l, j, v, ndec(p, j), pf_left(T, p, l, r, pf)), pf_right(T, p, l, r, pf))
    case 1n+ +p TNode{+l, +r} False{}:
      L.and_intro(perfect(T, p, l), perfect(T, p, tupd(T, p, r, Nat.sub(j, SC.pow2(p)), v, ndec(p, Nat.sub(j, SC.pow2(p))))), pf_left(T, p, l, r, pf), tupd_perfect(T, p, r, Nat.sub(j, SC.pow2(p)), v, ndec(p, Nat.sub(j, SC.pow2(p))), pf_right(T, p, l, r, pf)))

Uses (11):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.sub
  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=ndec
  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=pf_left
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/array.bend&name=pf_right
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/array.bend&name=tupd
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/logic.bend&name=and_intro
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend&name=pow2