List.replicate_add: 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 53-58 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=53&end_line=58

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

def replicate_add(-A: Data, +m: Nat, +n: Nat, +x: A) -> {SC.append(A, SC.replicate(A, m, x), SC.replicate(A, n, x)) == SC.replicate(A, Nat.add(m, n), x) : List<&2, A>}:
  match m:
    case 0n:
      {==}
    case 1n+p:
      cons_cong(A, x, SC.append(A, SC.replicate(A, p, x), SC.replicate(A, n, x)), SC.replicate(A, Nat.add(p, n), x), replicate_add(A, p, n, x))

Uses (6):
  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.add
  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/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=replicate