List.internal_all_eq_not_any_not: def of bend-mathlib@0.8.1.0
Import: import bend-mathlib@0.8.1.0/list.bend as List
Lines 2030-2039 of bend-mathlib@0.8.1.0/list.bend: https://jend.leeeet.dev/read.txt?path=bend-mathlib@0.8.1.0/list.bend&start_line=2030&end_line=2039

import Base

def internal_all_eq_not_any_not(~a: Quant, ~A: Kind(a), ~f: A -> Bool, xs: List<a, A>) -> {List.all(~a, ~A, ~f, xs) == Bool.not(List.any(~a, ~A, ~(x => Bool.not(f(x))), xs)) : Bool}:
  match xs:
    case Nil{}:
      {==}
    case h <> t:
      +v = f(h)
      %internal_all_cons_test(~a, ~A, ~f, h, t, v, {==}) : {_ == Bool.not(List.any(~a, ~A, ~(x => Bool.not(f(x))), h <> t)) : Bool}
      %internal_any_cons_test(~a, ~A, ~(x => Bool.not(f(x))), h, t, Bool.not(v), {==}) : {Bool.and(v, List.all(~a, ~A, ~f, t)) == Bool.not(_) : Bool}
      %Equal.sym(Bool, List.all(~a, ~A, ~f, t), Bool.not(List.any(~a, ~A, ~(x => Bool.not(f(x))), t)), internal_all_eq_not_any_not(~a, ~A, ~f, t)) : {Bool.and(v, _) == Bool.not(Bool.or(Bool.not(v), List.any(~a, ~A, ~(x => Bool.not(f(x))), t))) : Bool}
      internal_and_not_eq_not_or_not(v, List.any(~a, ~A, ~(x => Bool.not(f(x))), t))

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=Bool.not
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool.or
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List.all
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List.any
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/list.bend&name=internal_all_cons_test
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/list.bend&name=internal_and_not_eq_not_or_not
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/list.bend&name=internal_any_cons_test