PROOF.bool.and3: def of bend-osdev-caps@0.1.0.0
Import: import bend-osdev-caps@0.1.0.0/PROOF.bend as PROOF
Lines 68-77 of bend-osdev-caps@0.1.0.0/PROOF.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-caps@0.1.0.0/PROOF.bend&start_line=68&end_line=77

import Base

def bool.and3(+x: Bool, +y: Bool, +z: Bool) -> {x == True{} : Bool} -> {y == True{} : Bool} -> {z == True{} : Bool} -> {Bool.and(x, Bool.and(y, z)) == True{} : Bool}:
  match x y z:
    case True{} True{} True{}:
      hx => hy => hz => {==}
    case False{} y z:
      hx => hy => hz => bits.absurd(Bool.and(False{}, Bool.and(y, z)), hx)
    case True{} False{} z:
      hx => hy => hz => bits.absurd(Bool.and(True{}, Bool.and(False{}, z)), hy)
    case True{} True{} False{}:
      hx => hy => hz => bits.absurd(False{}, hz)

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=bend-osdev-caps@0.1.0.0/PROOF.bend&name=bits.absurd