Hash.bucket_le: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/math/hash/hash.bend as Hash
Lines 45-47 of bend-collections-laws-math@1.0.0.0/proofs/math/hash/hash.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/hash/hash.bend&start_line=45&end_line=47

import Base
import bend-collections-laws-math@1.0.0.0/src/math/hash.bend as HS
import bend-collections-laws-math@1.0.0.0/proofs/lib/u32div.bend as UD

# THEOREM: a bucket never exceeds the mask.
def bucket_le(+w: U32, +mask: U32) -> {Nat.is_le(UD.v(HS.bucket(w, mask)), UD.v(mask)) == True{} : Bool}:
  and_le32(U32.xor(U32.mul(w, HS.phi32()), U32.shrn(U32.mul(w, HS.phi32()), 16n)), mask)

Uses (10):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  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=U32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.mul
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.shrn
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.xor
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/u32div.bend&name=v
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/hash/hash.bend&name=and_le32
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/hash.bend&name=bucket
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/hash.bend&name=phi32