DivisionCandidateBound.smaller_high: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/proofs/division_candidate_bound.bend as DivisionCandidateBound
Lines 14-17 of bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/proofs/division_candidate_bound.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/proofs/division_candidate_bound.bend&start_line=14&end_line=17

import Base
import bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/src/wide.bend as W
import bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/proofs/division_no_overflow.bend as Overflow

def smaller_high(r: U32, d: U32, high: {W.last(32n, Overflow.bits(d)) == False{} : Bool}, less: {U32.is_lt(r, d) == True{} : Bool}) -> {W.last(32n, Overflow.bits(r)) == False{} : Bool}:
  match r d:
    case U32{+a} U32{+b}:
      Overflow.high_monotone(31n, a, b, high, lt_le(Word.cmp(32n, a, b), less))

Uses (8):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  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=Word.cmp
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/proofs/division_candidate_bound.bend&name=lt_le
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/proofs/division_no_overflow.bend&name=bits
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/proofs/division_no_overflow.bend&name=high_monotone
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/src/wide.bend&name=last