U64div.div_signed: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/math/u64/u64div.bend as U64div
Lines 356-362 of bend-collections-laws-math@1.0.0.0/proofs/math/u64/u64div.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/u64/u64div.bend&start_line=356&end_line=362

import Base
import bend-collections-laws-math@1.0.0.0/src/math/u64.bend as U
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/spec/numeric.bend as S
import bend-collections-laws-math@1.0.0.0/proofs/math/u64/u64.bend as P

# THEOREM: div_small_signed is the specification's signed quotient
# (truncating toward zero), for 0 < d <= 2^20.
def div_signed(+a: U.U64, +d: U32, +hd0: {U32.is_zero(d) == False{} : Bool}, +hle: {U32.is_le(d, 1048576) == True{} : Bool}) -> {P.bits(U.div_small_signed(a, d)) == qs(P.bits(a), S.negative(P.bits(a)), d) : Word(64n)}:
  match a:
    case U.U64{+lo, +hi}:
      %Equal.sym(Bool, S.negative(W.pack(lo, hi)), U32.is_ge(hi, 2147483648), P.negative_pack(lo, hi)) : {P.bits(U.div_small_signed(U.U64{lo, hi}, d)) == qs(W.pack(lo, hi), _, d) : Word(64n)}
      signed_g(lo, hi, d, hd0, hle, U32.is_ge(hi, 2147483648), P.negative_pack(lo, hi))

Uses (15):
  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=U32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.is_ge
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.is_le
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.is_zero
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/spec/numeric.bend&name=negative
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/src/wide.bend&name=pack
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/u64/u64.bend&name=bits
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/u64/u64.bend&name=negative_pack
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/u64/u64div.bend&name=qs
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/u64/u64div.bend&name=signed_g
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/u64.bend&name=U64
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/u64.bend&name=div_small_signed