PROOF.h.absent_del: def of bend-kit-collections@0.1.4.1
Import: import bend-kit-collections@0.1.4.1/PROOF.bend as PROOF
Lines 2482-2493 of bend-kit-collections@0.1.4.1/PROOF.bend: https://jend.leeeet.dev/read.txt?path=bend-kit-collections@0.1.4.1/PROOF.bend&start_line=2482&end_line=2493

import Base
import bend-mathlib@0.7.4.0/bool.bend as MBool
import bend-kit-collections@0.1.4.1/LAWS.bend as Laws
import bend-kit-collections@0.1.4.1/hmap.bend as M

def h.absent_del(
  ~K: Data, ~V: Data, ~eq: K -> K -> Bool, xs: List<&2, M.Entry<K, V>>, +key: K, +k: K,
  ab: {Laws.hmap_absent(~K, ~V, ~eq, xs, key) == True{} : Bool}
) -> {Laws.hmap_absent(~K, ~V, ~eq, M.HMap.entries.del(~K, ~V, ~eq, xs, k), key) == True{} : Bool}:
  match xs:
    case Nil{}:
      {==}
    case Con{M.Entry{+key2, +val}, +rest}:
      +ab = ab
      h.absent_del.c(~K, ~V, ~eq, key2, val, rest, key, k, eq(k, key2), ab,
        h.absent_del(~K, ~V, ~eq, rest, key, k,
          MBool.eq_true_of_and_right(Bool.not(eq(key, key2)), Laws.hmap_absent(~K, ~V, ~eq, rest, key), ab)))

Uses (8):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool.not
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/LAWS.bend&name=hmap_absent
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/PROOF.bend&name=h.absent_del.c
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/hmap.bend&name=Entry
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/hmap.bend&name=HMap.entries.del
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/bool.bend&name=eq_true_of_and_right