Shuffle.nth_put: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/math/random/shuffle.bend as Shuffle
Lines 66-78 of bend-collections-laws-math@1.0.0.0/proofs/math/random/shuffle.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/random/shuffle.bend&start_line=66&end_line=78

import Base
import bend-collections-laws-math@1.0.0.0/src/math/random/rand.bend as R

# writing y at i keeps an element y at j
def nth_put(-A: Data, +xs: List<&2, A>, +i: Nat, +j: Nat, +y: A, +h: {R.nth(A, xs, j) == Some{y} : Maybe<&2, A>}) -> {R.nth(A, R.put(A, xs, i, y), j) == Some{y} : Maybe<&2, A>}:
  match xs i j:
    case Nil{} _ _:
      Empty.absurd({R.nth(A, R.put(A, Nil{}, i, y), j) == Some{y} : Maybe<&2, A>}, none_some(A, y, h))
    case Con{+hd, +t} 0n 0n:
      {==}
    case Con{+hd, +t} 0n 1n+q:
      h
    case Con{+hd, +t} 1n+r 0n:
      h
    case Con{+hd, +t} 1n+r 1n+q:
      nth_put(A, t, r, q, y, h)

Uses (7):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Empty.absurd
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Maybe
  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/shuffle.bend&name=none_some
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/random/rand.bend&name=nth
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/random/rand.bend&name=put