PROOF.h.wf_put.lf: def of bend-kit-collections@0.1.4.1
Import: import bend-kit-collections@0.1.4.1/PROOF.bend as PROOF
Lines 3755-3768 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=3755&end_line=3768

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.lf(
  ~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},
  +p: Nat, +mask: U32, +o: U32, +es: List<&2, M.Entry<K, V>>, +k: K, +v: V,
  hs: {Laws.hmap_hashed(~K, ~V, ~hash, es, o) == True{} : Bool},
  ds: {Laws.hmap_distinct(~K, ~V, ~eq, es) == True{} : Bool},
  b: Bool, eb: {b == U32.is_eq(o, hash(k)) : Bool},
  sp: {h.WF(~K, ~V, ~hash, ~eq, 1n+p, h.S(~K, ~V, ~eq, 1n+p, mask, o, es, hash(k), k, v)) == True{} : Bool}
) -> {h.WF(~K, ~V, ~hash, ~eq, 1n+p, h.pl(~K, ~V, ~eq, b, p, mask, o, es, hash(k), k, v)) == True{} : Bool}:
  match b:
    case True{}:
      MBool.and_eq_true(Laws.hmap_hashed(~K, ~V, ~hash, M.HMap.entries.put(~K, ~V, ~eq, es, k, v), o), Laws.hmap_distinct(~K, ~V, ~eq, M.HMap.entries.put(~K, ~V, ~eq, es, k, v)), h.hashed_put(~K, ~V, ~hash, ~eq, es, o, k, v, h.sb(True{}, U32.is_eq(o, hash(k)), eb), hs), h.distinct_put(~K, ~V, ~eq, ~refl, ~sound, es, k, v, ds))
    case False{}:
      sp

Uses (16):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List
  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.is_eq
  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.S
  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.hashed_put
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/PROOF.bend&name=h.pl
  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=and_eq_true