~/jendhub

def perm_perm

bend-collections-laws-math@1.0.0.0 · proofs/math/random/shuffle.bend:150

import bend-collections-laws-math@1.0.0.0/proofs/math/random/shuffle.bend as Shuffle
import Base
import bend-collections-laws-math@1.0.0.0/src/math/u64.bend as W
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/spec/math/random/rand.bend as SR

150# THEOREM (Perm.permutation)
151def 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}:
152  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)),
153    shuffle_perm(~Nat, ~Nat, ~Nat.is_eq, ~S, ~next, s, R.range(n), i),
154    range_occ(n, [], i))

Uses (16)

Used by (1)