List.internal_all_if: def of bend-mathlib@0.8.1.0
Import: import bend-mathlib@0.8.1.0/list.bend as List
Lines 532-538 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=532&end_line=538

import Base

# Base 2.0.38 short-circuits each through a thunk (List.all.if, List.any.if, List.find.if), so the cons step is proved by cases on the head's test.
def internal_all_if(b: Bool, -r: Bool) -> {Bool.and(b, r) == List.all.if(u => r, b) : Bool}:
  match b:
    case False{}:
      {==}
    case True{}:
      {==}

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