PROOF.h.distinct_put.c: def of bend-kit-collections@0.1.4.1
Import: import bend-kit-collections@0.1.4.1/PROOF.bend as PROOF
Lines 2412-2425 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=2412&end_line=2425

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.distinct_put.c(
  ~K: Data, ~V: Data, ~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},
  +key: K, +val: V, +rest: List<&2, M.Entry<K, V>>, +k: K, +v: V, b: Bool, eb: {b == eq(k, key) : Bool},
  +ds: {Laws.hmap_distinct(~K, ~V, ~eq, M.Entry{key, val} <> rest) == True{} : Bool},
  ih: {Laws.hmap_distinct(~K, ~V, ~eq, M.HMap.entries.put(~K, ~V, ~eq, rest, k, v)) == True{} : Bool}
) -> {Laws.hmap_distinct(~K, ~V, ~eq, h.epc(~K, ~V, ~eq, b, key, val, rest, k, v)) == True{} : Bool}:
  match b:
    case True{}:
      ds
    case False{}:
      MBool.and_eq_true(Laws.hmap_absent(~K, ~V, ~eq, M.HMap.entries.put(~K, ~V, ~eq, rest, k, v), key), Laws.hmap_distinct(~K, ~V, ~eq, M.HMap.entries.put(~K, ~V, ~eq, rest, k, v)), h.absent_put(~K, ~V, ~eq, ~refl, ~sound, rest, key, k, v,
          MBool.eq_true_of_and_left(Laws.hmap_absent(~K, ~V, ~eq, rest, key), Laws.hmap_distinct(~K, ~V, ~eq, rest), ds),
          h.sb(False{}, eq(k, key), eb)), ih)

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=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/LAWS.bend&name=hmap_distinct
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/PROOF.bend&name=h.absent_put
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/PROOF.bend&name=h.epc
  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
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/bool.bend&name=eq_true_of_and_left