PROOF.h.absent_del.c: def of bend-kit-collections@0.1.4.1
Import: import bend-kit-collections@0.1.4.1/PROOF.bend as PROOF
Lines 2470-2480 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=2470&end_line=2480

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.c(
  ~K: Data, ~V: Data, ~eq: K -> K -> Bool, +key2: K, +val: V,
  +rest: List<&2, M.Entry<K, V>>, +key: K, +k: K, b: Bool,
  +ab: {Laws.hmap_absent(~K, ~V, ~eq, M.Entry{key2, val} <> rest, key) == True{} : Bool},
  ih: {Laws.hmap_absent(~K, ~V, ~eq, M.HMap.entries.del(~K, ~V, ~eq, rest, k), key) == True{} : Bool}
) -> {Laws.hmap_absent(~K, ~V, ~eq, h.edc(~K, ~V, ~eq, b, key2, val, rest, k), key) == True{} : Bool}:
  match b:
    case True{}:
      MBool.eq_true_of_and_right(Bool.not(eq(key, key2)), Laws.hmap_absent(~K, ~V, ~eq, rest, key), ab)
    case False{}:
      MBool.and_eq_true(Bool.not(eq(key, key2)), Laws.hmap_absent(~K, ~V, ~eq, M.HMap.entries.del(~K, ~V, ~eq, rest, k), key), MBool.eq_true_of_and_left(Bool.not(eq(key, key2)), Laws.hmap_absent(~K, ~V, ~eq, rest, key), ab), ih)

Uses (10):
  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.edc
  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=and_eq_true
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/bool.bend&name=eq_true_of_and_left
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/bool.bend&name=eq_true_of_and_right