ProofPcg.xs: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/math/random/proof_pcg.bend as ProofPcg
Lines 42-46 of bend-collections-laws-math@1.0.0.0/proofs/math/random/proof_pcg.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/random/proof_pcg.bend&start_line=42&end_line=46

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/spec/math/w64.bend as SW
import bend-collections-laws-math@1.0.0.0/spec/math/random/pcg.bend as SP
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/pcg.bend as P
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/w64sh.bend as SH
import bend-collections-laws-math@1.0.0.0/proofs/math/random/pcg/xor.bend as XO

# x ^ (x >> k)
def xs(+a: WU.U64, +k: Nat) -> {SW.value(P.xor64(a, X.shr(a, k))) == SP.xor_bits(64n, SW.value(a), C.high(k, SW.value(a))) : Nat}:
  Equal.trans(Nat, SW.value(P.xor64(a, X.shr(a, k))), SP.xor_bits(64n, SW.value(a), SW.value(X.shr(a, k))), SP.xor_bits(64n, SW.value(a), C.high(k, SW.value(a))),
    XO.xor64_value(a, X.shr(a, k)),
    Equal.cong(Nat, Nat, z => SP.xor_bits(64n, SW.value(a), z), SW.value(X.shr(a, k)), C.high(k, SW.value(a)), SH.shr_value(a, k)))

Uses (11):
  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=bend-collections-laws-math@1.0.0.0/proofs/math/random/pcg/xor.bend&name=xor64_value
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/typed/w64sh.bend&name=shr_value
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/lib/common.bend&name=high
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/math/random/pcg.bend&name=xor_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/pcg.bend&name=xor64
  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=shr