Hash.and_le32: 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 38-43 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=38&end_line=43

import Base
import bend-collections-laws-math@1.0.0.0/proofs/lib/word.bend as WD
import bend-collections-laws-math@1.0.0.0/proofs/lib/u32div.bend as UD

def and_le32(+x: U32, +m: U32) -> {Nat.is_le(UD.v(U32.and(x, m)), UD.v(m)) == True{} : Bool}:
  match x m:
    case U32{+a} U32{+b}:
      %Equal.sym(Nat, UD.v(U32{Word.and(32n, a, b)}), WD.uw(32n, Word.and(32n, a, b)), UD.vw(Word.and(32n, a, b))) : {Nat.is_le(_, UD.v(U32{b})) == True{} : Bool}
      %Equal.sym(Nat, UD.v(U32{b}), WD.uw(32n, b), UD.vw(b)) : {Nat.is_le(WD.uw(32n, Word.and(32n, a, b)), _) == True{} : Bool}
      and_le(32n, a, b)

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=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.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.and
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.and
  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/lib/u32div.bend&name=vw
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/word.bend&name=uw
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/hash/hash.bend&name=and_le