List.sc_take_rep: 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 395-404 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=395&end_line=404

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_rep(-A: Data, +m: Nat, +x: A, +n: Nat, +h: {Nat.is_le(n, m) == True{} : Bool}) -> {SC.take(A, SC.replicate(A, m, x), n) == SC.replicate(A, n, x) : List<&2, A>}:
  match m n:
    case 0n 0n:
      {==}
    case 0n 1n+k:
      Empty.absurd({SC.take(A, Nil{}, 1n+k) == SC.replicate(A, 1n+k, x) : List<&2, A>}, L.false_true(h))
    case 1n+j 0n:
      {==}
    case 1n+j 1n+k:
      cons_cong(A, x, SC.take(A, SC.replicate(A, j, x), k), SC.replicate(A, k, x), sc_take_rep(A, j, x, k, h))

Uses (9):
  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/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=replicate
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend&name=take