Uint64n.pow2_value: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/math/random/uint64n.bend as Uint64n
Lines 101-108 of bend-collections-laws-math@1.0.0.0/proofs/math/random/uint64n.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/random/uint64n.bend&start_line=101&end_line=108

import Base
import bend-collections-laws-math@1.0.0.0/spec/math/w64.bend as SW
import bend-collections-laws-math@1.0.0.0/spec/math/random/rand.bend as SR
import bend-collections-laws-math@1.0.0.0/src/math/u64.bend as WU
import bend-collections-laws-math@1.0.0.0/src/math/w64.bend as X
import bend-collections-laws-math@1.0.0.0/src/math/random/rand.bend as R
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/w64add.bend as WA
import bend-collections-laws-math@1.0.0.0/proofs/math/random/bits.bend as BI

# the power-of-two test is n & (n - 1) == 0
def pow2_value(+n: WU.U64, +m: Nat, +hv: {SW.value(n) == 1n+m : Nat}) -> {R.is_pow2(n) == Nat.is_eq(SR.and_bits(64n, 1n+m, m), 0n) : Bool}:
  Equal.trans(Bool, R.is_pow2(n), Nat.is_eq(SW.value(R.and64(n, X.sub(n, one64()))), 0n), Nat.is_eq(SR.and_bits(64n, 1n+m, m), 0n),
    WA.is_zero_value(R.and64(n, X.sub(n, one64()))),
    %Equal.sym(Nat, SW.value(R.and64(n, X.sub(n, one64()))), SR.and_bits(64n, SW.value(n), SW.value(X.sub(n, one64()))), BI.and64_value(n, X.sub(n, one64()))) : {Nat.is_eq(_, 0n) == Nat.is_eq(SR.and_bits(64n, 1n+m, m), 0n) : Bool}
    %Equal.sym(Nat, SW.value(n), 1n+m, hv) : {Nat.is_eq(SR.and_bits(64n, _, SW.value(X.sub(n, one64()))), 0n) == Nat.is_eq(SR.and_bits(64n, 1n+m, m), 0n) : Bool}
    %Equal.sym(Nat, SW.value(X.sub(n, one64())), m, pred_value(n, m, hv)) : {Nat.is_eq(SR.and_bits(64n, 1n+m, _), 0n) == Nat.is_eq(SR.and_bits(64n, 1n+m, m), 0n) : Bool}
    {==})

Uses (15):
  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_eq
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/random/bits.bend&name=and64_value
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/random/uint64n.bend&name=one64
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/random/uint64n.bend&name=pred_value
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/typed/w64add.bend&name=is_zero_value
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/math/random/rand.bend&name=and_bits
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/math/w64.bend&name=value
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/random/rand.bend&name=and64
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/random/rand.bend&name=is_pow2
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/u64.bend&name=U64
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/w64.bend&name=sub