List.nth_append_right: 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 71-79 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=71&end_line=79

import Base
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/logic.bend as L
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend as N
import bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend as SC

def nth_append_right(-A: Data, +xs: List<&2, A>, +ys: List<&2, A>, +i: Nat, +h: {Nat.is_le(SC.length(A, xs), i) == True{} : Bool}) -> {SC.nth(A, SC.append(A, xs, ys), i) == SC.nth(A, ys, Nat.sub(i, SC.length(A, xs))) : Maybe<&2, A>}:
  match xs i:
    case Nil{} _:
      %Equal.sym(Nat, Nat.sub(i, 0n), i, N.sub_zero(i)) : {SC.nth(A, ys, i) == SC.nth(A, ys, _) : Maybe<&2, A>}
      {==}
    case Con{h1, t} 0n:
      Empty.absurd({SC.nth(A, SC.append(A, Con{h1, t}, ys), 0n) == SC.nth(A, ys, Nat.sub(0n, 1n+SC.length(A, t))) : Maybe<&2, A>}, L.false_true(h))
    case Con{h1, t} 1n+p:
      nth_append_right(A, t, ys, p, h)

Uses (13):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Empty.absurd
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  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=Base/base.bend&name=Nat.is_le
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.sub
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/logic.bend&name=false_true
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend&name=sub_zero
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend&name=append
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend&name=length
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend&name=nth