ProofIndex.hi_idx: law of lawful-arrays@0.1.0.0
Import: import lawful-arrays@0.1.0.0/proof_index.bend as ProofIndex
Lines 97-104 of lawful-arrays@0.1.0.0/proof_index.bend: https://jend.leeeet.dev/read.txt?path=lawful-arrays@0.1.0.0/proof_index.bend&start_line=97&end_line=104

import Base

law hi_idx:
  for +n: U32
  for +i: U32
  for +p: Nat
  for +hn: {U32.to_nat(n) == Nat.pow(2n, 1n+p) : Nat}
  for +hi: {Nat.is_lt(U32.to_nat(i), Nat.pow(2n, 1n+p)) == True{} : Bool}
  for +hz: {U32.is_lt(i, U32.shr(n)) == False{} : Bool}
  {Nat.is_lt(U32.to_nat(U32.sub(i, U32.shr(n))), Nat.pow(2n, p)) == True{} : Bool}

Uses (17):
  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.add
  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=Nat.pow
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.sub
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.is_lt
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.shr
  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=lawful-arrays@0.1.0.0/proof_base.bend&name=lt_sub
  https://jend.leeeet.dev/definition.txt?path=lawful-arrays@0.1.0.0/proof_base.bend&name=pow_succ
  https://jend.leeeet.dev/definition.txt?path=lawful-arrays@0.1.0.0/proof_base.bend&name=subst
  https://jend.leeeet.dev/definition.txt?path=lawful-arrays@0.1.0.0/proof_index.bend&name=hi_nlt
  https://jend.leeeet.dev/definition.txt?path=lawful-arrays@0.1.0.0/proof_index.bend&name=hi_sub