PROOF.h.wf_del: def of bend-kit-collections@0.1.4.1
Import: import bend-kit-collections@0.1.4.1/PROOF.bend as PROOF
Lines 3847-3878 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=3847&end_line=3878

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.wf_del(
  ~K: Data, ~V: Data, ~hash: K -> U32, ~eq: K -> K -> Bool,
  n: Nat, +mask: U32, m: M.HMap<K, V>, +hk: U32, +k: K,
  +wf: {h.WF(~K, ~V, ~hash, ~eq, n, m) == True{} : Bool}
) -> {h.WF(~K, ~V, ~hash, ~eq, n, h.D(~K, ~V, ~eq, n, mask, m, hk, k)) == True{} : Bool}:
  match n:
    case 0n:
      match m:
        case M.HNil{}:
          {==}
        case M.HLeaf{+o, +es}:
          h.wf_leaf(~K, ~V, ~hash, ~eq, 0n, o, M.HMap.entries.del(~K, ~V, ~eq, es, k),
            h.distinct_del(~K, ~V, ~eq, es, k, wf))
        case M.HBranch{lo, hi}:
          wf
    case 1n+(+p):
      match m:
        case M.HNil{}:
          {==}
        case M.HLeaf{+o, +es}:
          h.wf_del.lf(~K, ~V, ~hash, ~eq, p, o, es, k,
            MBool.eq_true_of_and_left(Laws.hmap_hashed(~K, ~V, ~hash, es, o), Laws.hmap_distinct(~K, ~V, ~eq, es), wf),
            MBool.eq_true_of_and_right(Laws.hmap_hashed(~K, ~V, ~hash, es, o), Laws.hmap_distinct(~K, ~V, ~eq, es), wf),
            U32.is_eq(o, hk))
        case M.HBranch{+lo, +hi}:
          h.wf_del.br(~K, ~V, ~hash, ~eq, p, mask, lo, hi, hk, k, U32.is_eq((hk .&. mask : U32), 0),
            MBool.eq_true_of_and_left(h.WF(~K, ~V, ~hash, ~eq, p, lo), h.WF(~K, ~V, ~hash, ~eq, p, hi), wf),
            MBool.eq_true_of_and_right(h.WF(~K, ~V, ~hash, ~eq, p, lo), h.WF(~K, ~V, ~hash, ~eq, p, hi), wf),
            h.wf_del(~K, ~V, ~hash, ~eq, p, (mask << 1n : U32), lo, hk, k,
              MBool.eq_true_of_and_left(h.WF(~K, ~V, ~hash, ~eq, p, lo), h.WF(~K, ~V, ~hash, ~eq, p, hi), wf)),
            h.wf_del(~K, ~V, ~hash, ~eq, p, (mask << 1n : U32), hi, hk, k,
              MBool.eq_true_of_and_right(h.WF(~K, ~V, ~hash, ~eq, p, lo), h.WF(~K, ~V, ~hash, ~eq, p, hi), wf)))

Uses (18):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.and
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.is_eq
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.shln
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/LAWS.bend&name=hmap_distinct
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/LAWS.bend&name=hmap_hashed
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/PROOF.bend&name=h.D
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/PROOF.bend&name=h.WF
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/PROOF.bend&name=h.distinct_del
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/PROOF.bend&name=h.wf_del.br
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/PROOF.bend&name=h.wf_del.lf
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/PROOF.bend&name=h.wf_leaf
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/hmap.bend&name=HMap
  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_left
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/bool.bend&name=eq_true_of_and_right