U64div.and32: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/math/u64/u64div.bend as U64div
Lines 68-69 of bend-collections-laws-crypto@1.0.0.0/proofs/math/u64/u64div.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/math/u64/u64div.bend&start_line=68&end_line=69

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

def and32(+k: Nat, +x: U32, +m: U32, +hm: {m == U32{WD.mask(32n, k)} : U32}) -> {UD.v(x) == Nat.add(UD.v(U32.and(x, m)), WD.sc(k, hp32(k, x))) : Nat}:
  L.subst(U32, z => {UD.v(x) == Nat.add(UD.v(U32.and(x, z)), WD.sc(k, hp32(k, x))) : Nat}, U32{WD.mask(32n, k)}, m, Equal.sym(U32, m, U32{WD.mask(32n, k)}, hm), and32w(k, x))

Uses (11):
  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.add
  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=bend-collections-laws-crypto@1.0.0.0/proofs/lib/logic.bend&name=subst
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/u32div.bend&name=v
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/word.bend&name=mask
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/word.bend&name=sc
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/math/u64/u64div.bend&name=and32w
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/math/u64/u64div.bend&name=hp32