PROOF.AP.new_leaves.go: def of bend-osdev-array@0.1.0.1
Import: import bend-osdev-array@0.1.0.1/PROOF.bend as PROOF
Lines 1261-1269 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=1261&end_line=1269

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.new_leaves.go(-T: Data, +d: Nat, +v: T) -> {A.Arrays.leaves(T, Array.new(T, d, v)) == List.replicate(T, A.Arrays.slots(d), v) : List<&2, T>}:
  match d:
    case 0n:
      {==}
    case 1n+ +p:
      +s = A.Arrays.slots(p)
      %Equal.sym(List<&2, T>, A.Arrays.leaves(T, Array.new(T, p, v)), List.replicate(T, s, v), AP.new_leaves.go(T, p, v)) : {List.append(&2, T, _, _) == List.replicate(T, Nat.double(s), v) : List<&2, T>}
      %Equal.sym(Nat, Nat.double(s), Nat.add(s, s), UL.nat_double(s)) : {List.append(&2, T, List.replicate(T, s, v), List.replicate(T, s, v)) == List.replicate(T, _, v) : List<&2, T>}
      Equal.sym(List<&2, T>, List.replicate(T, Nat.add(s, s), v), List.append(&2, T, List.replicate(T, s, v), List.replicate(T, s, v)), AP.rep_add(T, s, s, v))

Uses (12):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Array.new
  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.append
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List.replicate
  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.rep_add
  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