PROOF.AP.tof_leaves: def of bend-osdev-array@0.1.0.1
Import: import bend-osdev-array@0.1.0.1/PROOF.bend as PROOF
Lines 1435-1446 of bend-osdev-array@0.1.0.1/PROOF.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-array@0.1.0.1/PROOF.bend&start_line=1435&end_line=1446

import Base
import bend-osdev-array@0.1.0.1/array.bend as A
import bend-osdev-u32@0.1.0.0/LAWS.bend as UL

def AP.tof_leaves(-T: Data, +d: Nat, +xs: List<&2, T>, +f: T, +h: {List.length(&2, T, xs) == A.Arrays.slots(d) : Nat}) -> {A.Arrays.leaves(T, AP.build(T, AP.tof(T, d, xs, f))) == xs : List<&2, T>}:
  match d:
    case 0n:
      AP.one_elem(T, xs, f, h)
    case 1n+ +p:
      +s = A.Arrays.slots(p)
      +l = List.take(&2, T, xs, s)
      +r = List.drop(&2, T, xs, s)
      +h2 = Equal.trans(Nat, List.length(&2, T, xs), Nat.double(s), Nat.add(s, s), h, UL.nat_double(s))
      %Equal.sym(List<&2, T>, A.Arrays.leaves(T, AP.build(T, AP.tof(T, p, l, f))), l, AP.tof_leaves(T, p, l, f, AP.len_take(T, xs, s, s, h2))) : {List.append(&2, T, _, A.Arrays.leaves(T, AP.build(T, AP.tof(T, p, r, f)))) == xs : List<&2, T>}
      %Equal.sym(List<&2, T>, A.Arrays.leaves(T, AP.build(T, AP.tof(T, p, r, f))), r, AP.tof_leaves(T, p, r, f, AP.len_drop(T, xs, s, s, h2))) : {List.append(&2, T, l, _) == xs : List<&2, T>}
      AP.take_drop(T, xs, s)

Uses (19):
  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.append
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List.drop
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List.length
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List.take
  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=Nat.double
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-array@0.1.0.1/PROOF.bend&name=AP.build
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-array@0.1.0.1/PROOF.bend&name=AP.len_drop
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-array@0.1.0.1/PROOF.bend&name=AP.len_take
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-array@0.1.0.1/PROOF.bend&name=AP.one_elem
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-array@0.1.0.1/PROOF.bend&name=AP.take_drop
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-array@0.1.0.1/PROOF.bend&name=AP.tof
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-array@0.1.0.1/array.bend&name=Arrays.leaves
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-array@0.1.0.1/array.bend&name=Arrays.slots
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/LAWS.bend&name=nat_double