Lists.take_append_left: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/blake/blake3/lists.bend as Lists
Lines 54-59 of bend-collections-laws-crypto@1.0.0.0/proofs/crypto/blake/blake3/lists.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/blake/blake3/lists.bend&start_line=54&end_line=59

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 take_append_left(-A: Data, +xs: List<&2,A>, +ys: List<&2,A>, +k: Nat, +h: {Nat.is_le(k,SC.length(A,xs)) == True{} : Bool}) -> {SC.take(A,SC.append(A,xs,ys),k) == SC.take(A,xs,k) : List<&2,A>}:
  match xs k:
    case Nil{} 0n: 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),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/crypto/blake/blake3/lists.bend&name=cons_cong
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/blake/blake3/lists.bend&name=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