PROOF.h.wf_put: def of bend-kit-collections@0.1.4.1
Import: import bend-kit-collections@0.1.4.1/PROOF.bend as PROOF
Lines 3784-3818 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=3784&end_line=3818

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_put(
  ~K: Data, ~V: Data, ~hash: K -> U32, ~eq: K -> K -> Bool, ~refl: @x: K -> {eq(x, x) == True{} : Bool},
  ~sound: @x: K -> @y: K -> {eq(x, y) == True{} : Bool} -> {x == y : K},
  n: Nat, +mask: U32, m: M.HMap<K, V>, +k: K, +v: V,
  +wf: {h.WF(~K, ~V, ~hash, ~eq, n, m) == True{} : Bool}
) -> {h.WF(~K, ~V, ~hash, ~eq, n, h.P(~K, ~V, ~eq, n, mask, m, hash(k), k, v)) == True{} : Bool}:
  match n:
    case 0n:
      match m:
        case M.HNil{}:
          {==}
        case M.HLeaf{o, es}:
          h.distinct_put(~K, ~V, ~eq, ~refl, ~sound, es, k, v, wf)
        case M.HBranch{lo, hi}:
          wf
    case 1n+(+p):
      match m:
        case M.HNil{}:
          h.wf_fresh(~K, ~V, ~hash, ~eq, 1n+p, k, v)
        case M.HLeaf{+o, +es}:
          h.wf_put.lf(~K, ~V, ~hash, ~eq, ~refl, ~sound, p, mask, o, es, k, v,
            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, hash(k)), {==},
            h.split_wf(~K, ~V, ~hash, ~eq, ~refl, ~sound, 1n+p, mask, o, es, k, v,
              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)))
        case M.HBranch{+lo, +hi}:
          h.wf_put.br(~K, ~V, ~hash, ~eq, p, mask, lo, hi, hash(k), k, v, U32.is_eq((hash(k) .&. 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_put(~K, ~V, ~hash, ~eq, ~refl, ~sound, p, (mask << 1n : U32), lo, k, v,
              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_put(~K, ~V, ~hash, ~eq, ~refl, ~sound, p, (mask << 1n : U32), hi, k, v,
              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.P
  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_put
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/PROOF.bend&name=h.split_wf
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/PROOF.bend&name=h.wf_fresh
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/PROOF.bend&name=h.wf_put.br
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/PROOF.bend&name=h.wf_put.lf
  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-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