Shuffle.perm_perm: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/math/random/shuffle.bend as Shuffle
Lines 150-154 of bend-collections-laws-crypto@1.0.0.0/proofs/math/random/shuffle.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/math/random/shuffle.bend&start_line=150&end_line=154

import Base
import bend-collections-laws-crypto@1.0.0.0/src/math/u64.bend as W
import bend-collections-laws-crypto@1.0.0.0/src/math/random/rand.bend as R
import bend-collections-laws-crypto@1.0.0.0/spec/math/random/rand.bend as SR

# THEOREM (Perm.permutation)
def perm_perm(~S: Data, ~next: S -> W.U64 & S, +s: S, +n: Nat, +i: Nat) -> {SR.occurrences(~Nat, ~Nat, ~Nat.is_eq, i, R.fst(List<&2, Nat>, S, R.perm(~S, ~next, s, n))) == SR.b2n(Nat.is_lt(i, n)) : Nat}:
  Equal.trans(Nat, SR.occurrences(~Nat, ~Nat, ~Nat.is_eq, i, R.fst(List<&2, Nat>, S, R.shuffle(~Nat, ~S, ~next, s, R.range(n)))), SR.occurrences(~Nat, ~Nat, ~Nat.is_eq, i, R.range_go(n, [])), SR.b2n(Nat.is_lt(i, n)),
    shuffle_perm(~Nat, ~Nat, ~Nat.is_eq, ~S, ~next, s, R.range(n), i),
    range_occ(n, [], i))

Uses (16):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.trans
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List
  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=Base/base.bend&name=Nat.is_lt
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Pair
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/math/random/shuffle.bend&name=range_occ
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/math/random/shuffle.bend&name=shuffle_perm
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/math/random/rand.bend&name=b2n
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/math/random/rand.bend&name=occurrences
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/math/random/rand.bend&name=fst
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/math/random/rand.bend&name=perm
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/math/random/rand.bend&name=range
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/math/random/rand.bend&name=range_go
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/math/random/rand.bend&name=shuffle
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/math/u64.bend&name=U64