PROOF.AP.slots_le: def of bend-osdev-array@0.1.0.1
Import: import bend-osdev-array@0.1.0.1/PROOF.bend as PROOF
Lines 797-806 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=797&end_line=806

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

def AP.slots_le(d: Nat, n: Nat, h: {Nat.is_le(d, n) == True{} : Bool}) -> {Nat.is_le(A.Arrays.slots(d), A.Arrays.slots(n)) == True{} : Bool}:
  match d n:
    case 0n 0n:
      {==}
    case 0n 1n+ +q:
      AP.dpos(A.Arrays.slots(q), AP.slots_pos(q))
    case 1n+p 0n:
      Empty.absurd({Nat.is_le(A.Arrays.slots(1n+p), A.Arrays.slots(0n)) == True{} : Bool}, AP.ft(h))
    case 1n+ +p 1n+ +q:
      AP.double_le(A.Arrays.slots(p), A.Arrays.slots(q), AP.slots_le(p, q, h))

Uses (9):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Empty.absurd
  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_le
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-array@0.1.0.1/PROOF.bend&name=AP.double_le
  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/PROOF.bend&name=AP.ft
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-array@0.1.0.1/PROOF.bend&name=AP.slots_pos
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-array@0.1.0.1/array.bend&name=Arrays.slots