TwoList.len_drop: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/lib/two_list.bend as TwoList
Lines 26-33 of bend-collections-laws-math@1.0.0.0/proofs/lib/two_list.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/two_list.bend&start_line=26&end_line=33

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

def len_drop(-T: Data, +xs: List<&2, T>, +k: Nat) -> {SC.length(T, SC.drop(T, xs, k)) == Nat.sub(SC.length(T, xs), k) : Nat}:
  match xs k:
    case Nil{} _:
      Equal.sym(Nat, Nat.sub(0n, k), 0n, zero_sub(k))
    case Con{h, t} 0n:
      Equal.sym(Nat, Nat.sub(1n+SC.length(T, t), 0n), 1n+SC.length(T, t), N.sub_zero(1n+SC.length(T, t)))
    case Con{h, t} 1n+p:
      len_drop(T, t, p)

Uses (8):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  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.sub
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend&name=sub_zero
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/two_list.bend&name=zero_sub
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/lib/common.bend&name=drop
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/lib/common.bend&name=length