PROOF.AP.index_of_nat.go: def of bend-osdev-array@0.1.0.1
Import: import bend-osdev-array@0.1.0.1/PROOF.bend as PROOF
Lines 1319-1324 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=1319&end_line=1324

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

def AP.index_of_nat.go(+d: Nat, +hd: {Nat.is_lt(d, 32n) == True{} : Bool}, +k: Nat, +hk: {Nat.is_lt(k, A.Arrays.slots(d)) == True{} : Bool}) -> {A.Arrays.index(d, U32.from_nat(k)) == k : Nat}:
  +a = U32.from_nat(k)
  +fk = AP.from_nat(k, d, hk, AP.lt_le(d, 32n, hd))
  %Equal.sym(U32, U32.sub(U32.shln(1, d), 1), U32{AP.lm(32n, d)}, AP.mask_lm(d)) : {U32.to_nat(U32.and(a, _)) == k : Nat}
  %Equal.sym(U32, U32.and(a, U32{AP.lm(32n, d)}), a, AP.u32_and_id(a, d, AP.lt_rw_l(U32.to_nat(a), k, A.Arrays.slots(d), fk, hk))) : {U32.to_nat(_) == k : Nat}
  fk

Uses (18):
  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=Nat
  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=U32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.and
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.from_nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.shln
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.sub
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.to_nat
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-array@0.1.0.1/PROOF.bend&name=AP.from_nat
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-array@0.1.0.1/PROOF.bend&name=AP.lm
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-array@0.1.0.1/PROOF.bend&name=AP.lt_le
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-array@0.1.0.1/PROOF.bend&name=AP.lt_rw_l
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-array@0.1.0.1/PROOF.bend&name=AP.mask_lm
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-array@0.1.0.1/PROOF.bend&name=AP.u32_and_id
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-array@0.1.0.1/array.bend&name=Arrays.index
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-array@0.1.0.1/array.bend&name=Arrays.slots