U64div.mulp32: 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 130-133 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=130&end_line=133

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

# v(x * k) == 2^j v(x) when v(k) == 2^j and 2^j v(x) < 2^32
def mulp32(+one: Nat, +h1: {one == 1n : Nat}, +j: Nat, +x: U32, +k: U32, +hk: {UD.v(k) == WD.sc(j, one) : Nat}, +hb: {Nat.is_lt(WD.sc(j, UD.v(x)), WD.sc(32n, one)) == True{} : Bool}) -> {UD.v(U32.mul(x, k)) == WD.sc(j, UD.v(x)) : Nat}:
  +em = mul_pow(one, h1, j, UD.v(x), UD.v(k), hk)
  Equal.trans(Nat, UD.v(U32.mul(x, k)), Nat.mul(UD.v(x), UD.v(k)), WD.sc(j, UD.v(x)), mul32(one, h1, x, k, lt_eq(WD.sc(j, UD.v(x)), Nat.mul(UD.v(x), UD.v(k)), WD.sc(32n, one), Equal.sym(Nat, Nat.mul(UD.v(x), UD.v(k)), WD.sc(j, UD.v(x)), em), hb)), em)

Uses (13):
  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=Equal.trans
  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_lt
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.mul
  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=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/word.bend&name=sc
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/u64/u64div.bend&name=lt_eq
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/u64/u64div.bend&name=mul32
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/u64/u64div.bend&name=mul_pow