PROOF.h.hashed_put: def of bend-kit-collections@0.1.4.1
Import: import bend-kit-collections@0.1.4.1/PROOF.bend as PROOF
Lines 2454-2468 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=2454&end_line=2468

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.hashed_put(
  ~K: Data, ~V: Data, ~hash: K -> U32, ~eq: K -> K -> Bool,
  xs: List<&2, M.Entry<K, V>>, +o: U32, +k: K, +v: V,
  +hk: {U32.is_eq(o, hash(k)) == True{} : Bool},
  hs: {Laws.hmap_hashed(~K, ~V, ~hash, xs, o) == True{} : Bool}
) -> {Laws.hmap_hashed(~K, ~V, ~hash, M.HMap.entries.put(~K, ~V, ~eq, xs, k, v), o) == True{} : Bool}:
  match xs:
    case Nil{}:
      %h.sb(U32.is_eq(o, hash(k)), True{}, hk) : {Bool.and(_, True{}) == True{} : Bool}
      {==}
    case Con{M.Entry{+key, +val}, +rest}:
      +hs = hs
      h.hashed_put.c(~K, ~V, ~hash, ~eq, key, val, rest, o, k, v, eq(k, key), hs,
        h.hashed_put(~K, ~V, ~hash, ~eq, rest, o, k, v, hk,
          MBool.eq_true_of_and_right(U32.is_eq(o, hash(key)), Laws.hmap_hashed(~K, ~V, ~hash, rest, o), hs)))

Uses (11):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool.and
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.is_eq
  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.hashed_put.c
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/PROOF.bend&name=h.sb
  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.put
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/bool.bend&name=eq_true_of_and_right