List.sc_take_append_right: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/lib/list.bend as List
Lines 341-350 of bend-collections-laws-math@1.0.0.0/proofs/lib/list.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/list.bend&start_line=341&end_line=350

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

def sc_take_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.take(A, SC.append(A, xs, ys), i) == SC.append(A, xs, SC.take(A, ys, Nat.sub(i, SC.length(A, xs)))) : List<&2, A>}:
  match xs i:
    case Nil{} 0n:
      {==}
    case Nil{} 1n+j:
      {==}
    case Con{a, t} 0n:
      Empty.absurd({SC.take(A, SC.append(A, Con{a, t}, ys), 0n) == SC.append(A, Con{a, t}, SC.take(A, ys, Nat.sub(0n, 1n+SC.length(A, t)))) : List<&2, A>}, L.false_true(h))
    case Con{a, t} 1n+j:
      cons_cong(A, a, SC.take(A, SC.append(A, t, ys), j), SC.append(A, t, SC.take(A, ys, Nat.sub(j, SC.length(A, t)))), sc_take_append_right(A, t, ys, j, h))

Uses (11):
  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=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_le
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.sub
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/list.bend&name=cons_cong
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/logic.bend&name=false_true
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/lib/common.bend&name=append
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/lib/common.bend&name=length
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/lib/common.bend&name=take