PROOF.AP.slots_pos: def of bend-osdev-array@0.1.0.1
Import: import bend-osdev-array@0.1.0.1/PROOF.bend as PROOF
Lines 790-795 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=790&end_line=795

import Base
import bend-osdev-array@0.1.0.1/array.bend as A
import bend-osdev-u32@0.1.0.0/LAWS_order.bend as UO

def AP.slots_pos(d: Nat) -> {Nat.is_lt(0n, A.Arrays.slots(d)) == True{} : Bool}:
  match d:
    case 0n:
      {==}
    case 1n+ +p:
      UO.nat_lt_le_trans(0n, 1n, Nat.double(A.Arrays.slots(p)), {==}, AP.dpos(A.Arrays.slots(p), AP.slots_pos(p)))

Uses (7):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.double
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_lt
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-array@0.1.0.1/PROOF.bend&name=AP.dpos
  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_order.bend&name=nat_lt_le_trans