PROOF.AP.tnew_tof: def of bend-osdev-array@0.1.0.1
Import: import bend-osdev-array@0.1.0.1/PROOF.bend as PROOF
Lines 1502-1507 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=1502&end_line=1507

import Base
import bend-osdev-array@0.1.0.1/array.bend as A

def AP.tnew_tof(-T: Data, +d: Nat, +v: T) -> {AP.build(T, AP.tnew(T, d, v)) == AP.build(T, AP.tof(T, d, List.replicate(T, A.Arrays.slots(d), v), v)) : Array<T>}:
  +t = AP.tnew(T, d, v)
  +hp = Equal.trans(Bool, A.Arrays.is_perfect(T, d, AP.build(T, t)), A.Arrays.is_perfect(T, d, Array.new(T, d, v)), True{}, Equal.cong(Array<T>, Bool, a => A.Arrays.is_perfect(T, d, a), AP.build(T, t), Array.new(T, d, v), Equal.sym(Array<T>, Array.new(T, d, v), AP.build(T, t), AP.new_eq(T, d, v))), AP.new_perf(T, d, v))
  +hl = Equal.trans(List<&2, T>, A.Arrays.leaves(T, AP.build(T, t)), A.Arrays.leaves(T, Array.new(T, d, v)), List.replicate(T, A.Arrays.slots(d), v), Equal.cong(Array<T>, List<&2, T>, a => A.Arrays.leaves(T, a), AP.build(T, t), Array.new(T, d, v), Equal.sym(Array<T>, Array.new(T, d, v), AP.build(T, t), AP.new_eq(T, d, v))), AP.new_leaves.go(T, d, v))
  %hl : {AP.build(T, t) == AP.build(T, AP.tof(T, d, _, v)) : Array<T>}
  AP.tree_ext(T, d, t, v, hp)

Uses (19):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Array
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Array.new
  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.replicate
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  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.new_eq
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-array@0.1.0.1/PROOF.bend&name=AP.new_leaves.go
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-array@0.1.0.1/PROOF.bend&name=AP.new_perf
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-array@0.1.0.1/PROOF.bend&name=AP.tnew
  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/PROOF.bend&name=AP.tree_ext
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-array@0.1.0.1/array.bend&name=Arrays.is_perfect
  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