Xor.bit_bvd: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/math/random/pcg/xor.bend as Xor
Lines 22-28 of bend-collections-laws-math@1.0.0.0/proofs/math/random/pcg/xor.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/random/pcg/xor.bend&start_line=22&end_line=28

import Base
import bend-collections-laws-math@1.0.0.0/spec/lib/common.bend as C
import bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/spec/numeric.bend as S
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/width.bend as WW

# the low bit and the rest of bv(b) + 2 u
def bit_bvd(+b: Bool, +u: Nat) -> {C.bit(Nat.add(S.bit_value(b), Nat.double(u))) == S.bit_value(b) : Nat}:
  match b:
    case True{}:
      WW.bit_dbl(1n, u)
    case False{}:
      WW.bit_dbl(0n, u)

Uses (7):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  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=Nat.double
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/spec/numeric.bend&name=bit_value
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/typed/width.bend&name=bit_dbl
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/lib/common.bend&name=bit