Logs.ilog_bounds: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/math/natural/logs.bend as Logs
Lines 82-83 of bend-collections-laws-math@1.0.0.0/proofs/math/natural/logs.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/natural/logs.bend&start_line=82&end_line=83

import Base
import bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend as N
import bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/proofs/nat_algebra.bend as A

def ilog_bounds(+np: Nat, +bq: Nat) -> {Nat.is_le(Nat.pow(2n+bq, ilog_value(np, bq)), 1n+np) == True{} : Bool} & {Nat.is_lt(1n+np, Nat.pow(2n+bq, 1n+ilog_value(np, bq))) == True{} : Bool}:
  ilog_ok(1n+np, 1n+np, bq, 0n, 1n, Nat.is_le(1n, Nat.div(1n+np, 2n+bq)), {==}, N.lt_succ_le_succ(0n, 1n+np, {==}), {==}, A.add_zero(1n+np))

Uses (11):
  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.div
  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=Nat.pow
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Pair
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/proofs/nat_algebra.bend&name=add_zero
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend&name=lt_succ_le_succ
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/natural/logs.bend&name=ilog_ok
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/natural/logs.bend&name=ilog_value