List.sc_take_append_left: 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 330-339 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=330&end_line=339

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/spec/lib/common.bend as SC

def sc_take_append_left(-A: Data, +xs: List<&2, A>, +ys: List<&2, A>, +i: Nat, +h: {Nat.is_le(i, SC.length(A, xs)) == True{} : Bool}) -> {SC.take(A, SC.append(A, xs, ys), i) == SC.take(A, xs, i) : List<&2, A>}:
  match xs i:
    case Nil{} 0n:
      sc_take_zero(A, ys)
    case Nil{} 1n+j:
      Empty.absurd({SC.take(A, ys, 1n+j) == Nil{} : List<&2, A>}, L.false_true(h))
    case Con{a, t} 0n:
      {==}
    case Con{a, t} 1n+j:
      cons_cong(A, a, SC.take(A, SC.append(A, t, ys), j), SC.take(A, t, j), sc_take_append_left(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=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/proofs/lib/list.bend&name=sc_take_zero
  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/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=take