ProofPcg.xt: 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 80-83 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=80&end_line=83

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

# x ^ (x >> 48) for a word of value t
def xt(+H: WU.U64, +t: Nat, +ht: {SW.value(H) == t : Nat}) -> {SW.value(P.xor64(H, X.shr(H, 48n))) == SP.xor_bits(64n, t, C.high(48n, t)) : Nat}:
  Equal.trans(Nat, SW.value(P.xor64(H, X.shr(H, 48n))), SP.xor_bits(64n, SW.value(H), C.high(48n, SW.value(H))), SP.xor_bits(64n, t, C.high(48n, t)),
    xs48(H), Equal.cong(Nat, Nat, z => SP.xor_bits(64n, z, C.high(48n, z)), SW.value(H), t, ht))

Uses (10):
  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/proof_pcg.bend&name=xs48
  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