PROOF.AP.index_wrap.go: def of bend-osdev-array@0.1.0.1
Import: import bend-osdev-array@0.1.0.1/PROOF.bend as PROOF
Lines 1743-1749 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=1743&end_line=1749

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

def AP.index_wrap.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(Nat.add(A.Arrays.slots(d), k))) == k : Nat}:
  +s = A.Arrays.slots(d)
  +a = U32.from_nat(Nat.add(s, k))
  +hd1 = Equal.trans(Bool, Nat.is_le(1n+d, 32n), Nat.is_lt(d, 32n), True{}, AP.le_succ(d, 32n), hd)
  +fk = AP.from_nat(Nat.add(s, k), 1n+d, AP.wrap_lt(s, k, hk), hd1)
  %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}
  AP.u32_wrap(a, d, k, fk, hk, hd)

Uses (21):
  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=Equal.trans
  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.is_le
  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.le_succ
  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.mask_lm
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-array@0.1.0.1/PROOF.bend&name=AP.u32_wrap
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-array@0.1.0.1/PROOF.bend&name=AP.wrap_lt
  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