List.internal_all_if_and: def of bend-mathlib@0.8.1.0
Import: import bend-mathlib@0.8.1.0/list.bend as List
Lines 584-590 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=584&end_line=590

import Base

# The cons step of all_append, any_append and contains_append, given the step for the tail; proved by cases on the head's test.
def internal_all_if_and(b: Bool, -r: Bool, -s: Bool, -l: Bool, ih: {l == Bool.and(r, s) : Bool}) -> {List.all.if(u => l, b) == Bool.and(List.all.if(u => r, b), s) : Bool}:
  match b:
    case False{}:
      {==}
    case True{}:
      ih

Uses (3):
  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=List.all.if