U32.mask_pow2u: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/lib/u32.bend as U32
Lines 273-278 of bend-collections-laws-math@1.0.0.0/proofs/lib/u32.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/u32.bend&start_line=273&end_line=278

import Base
import bend-collections-laws-math@1.0.0.0/spec/lib/common.bend as SC

def mask_pow2u(+x: U32, +d: Nat, +hd: {Nat.is_lt(d, 32n) == True{} : Bool}, +hx: {Nat.is_lt(U32.to_nat(x), SC.pow2(d)) == True{} : Bool}) -> {U32.and(x, U32.sub(pow2u(d), 1)) == x : U32}:
  mask_word(x, U32.sub(pow2u(d), 1), d,
    Equal.trans(Nat, U32.to_nat(U32.sub(pow2u(d), 1)), Nat.sub(U32.to_nat(pow2u(d)), 1n), Nat.sub(SC.pow2(d), 1n),
      sub_nat(pow2u(d), 1, one_le_pow2u(d, hd)),
      Equal.cong(Nat, Nat, v => Nat.sub(v, 1n), U32.to_nat(pow2u(d)), SC.pow2(d), pow2u_value(d, hd))),
    hx)

Uses (16):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  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.is_lt
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.sub
  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=U32.sub
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.to_nat
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/u32.bend&name=mask_word
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/u32.bend&name=one_le_pow2u
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/u32.bend&name=pow2u
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/u32.bend&name=pow2u_value
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/u32.bend&name=sub_nat
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/lib/common.bend&name=pow2