PROOF.h.gp_other.lf: def of bend-kit-collections@0.1.4.1
Import: import bend-kit-collections@0.1.4.1/PROOF.bend as PROOF
Lines 3157-3172 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=3157&end_line=3172

import Base
import bend-kit-collections@0.1.4.1/hmap.bend as M

def h.gp_other.lf(
  ~K: Data, ~V: Data, ~hash: K -> U32, ~eq: K -> K -> 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>>, +h2: U32, +k2: K, +k: K, +v: V,
  +nk: {eq(k, k2) == False{} : Bool}, b: Bool,
  sp: {h.G(~K, ~V, ~eq, 1n+p, mask, h.S(~K, ~V, ~eq, 1n+p, mask, o, es, h2, k2, v), hash(k), k)
       == h.G(~K, ~V, ~eq, 1n+p, mask, M.HLeaf{o, es}, hash(k), k) : Maybe<&2, V>}
) -> {h.G(~K, ~V, ~eq, 1n+p, mask, h.pl(~K, ~V, ~eq, b, p, mask, o, es, h2, k2, v), hash(k), k)
      == h.G(~K, ~V, ~eq, 1n+p, mask, M.HLeaf{o, es}, hash(k), k) : Maybe<&2, V>}:
  match b:
    case True{}:
      h.bool_l(Maybe<&2, V>, U32.is_eq(o, hash(k)),
        h.EG(~K, ~V, ~eq, M.HMap.entries.put(~K, ~V, ~eq, es, k2, v), k), h.EG(~K, ~V, ~eq, es, k), None{},
        h.eg_put_other(~K, ~V, ~eq, ~sound, es, k2, k, v, nk))
    case False{}:
      sp

Uses (15):
  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=Maybe
  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/PROOF.bend&name=h.EG
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/PROOF.bend&name=h.G
  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.bool_l
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/PROOF.bend&name=h.eg_put_other
  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/hmap.bend&name=Entry
  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.put