U64div.mul_pow: 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 126-128 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=126&end_line=128

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/arith.bend as AR

# a scaled product c*k with v(k) == 2^j, as 2^j c
def mul_pow(+one: Nat, +h1: {one == 1n : Nat}, +j: Nat, +c: Nat, +kv: Nat, +hk: {kv == WD.sc(j, one) : Nat}) -> {Nat.mul(c, kv) == WD.sc(j, c) : Nat}:
  Equal.trans(Nat, Nat.mul(c, kv), Nat.mul(c, WD.sc(j, one)), WD.sc(j, c), Equal.cong(Nat, Nat, z => Nat.mul(c, z), kv, WD.sc(j, one), hk), AR.mul_sc1(j, one, h1, c))

Uses (6):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.cong
  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.mul
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/arith.bend&name=mul_sc1
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/word.bend&name=sc