List.sc_take_update: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/lib/list.bend as List
Lines 382-393 of bend-collections-laws-crypto@1.0.0.0/proofs/lib/list.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/list.bend&start_line=382&end_line=393

import Base
import bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend as SC

def sc_take_update(-A: Data, +xs: List<&2, A>, +i: Nat, +v: A, +n: Nat) -> {SC.take(A, SC.update(A, xs, i, v), n) == SC.update(A, SC.take(A, xs, n), i, v) : List<&2, A>}:
  match xs i n:
    case Nil{} _ _:
      {==}
    case Con{a, t} 0n 0n:
      {==}
    case Con{a, t} 1n+j 0n:
      {==}
    case Con{a, t} 0n 1n+m:
      {==}
    case Con{a, t} 1n+j 1n+m:
      cons_cong(A, a, SC.take(A, SC.update(A, t, j, v), m), SC.update(A, SC.take(A, t, m), j, v), sc_take_update(A, t, j, v, m))

Uses (5):
  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=bend-collections-laws-crypto@1.0.0.0/proofs/lib/list.bend&name=cons_cong
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend&name=take
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend&name=update