PROOF.valid.ap: def of bend-osdev-caps@0.1.0.0
Import: import bend-osdev-caps@0.1.0.0/PROOF.bend as PROOF
Lines 91-94 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=91&end_line=94

import Base
import bend-osdev-caps@0.1.0.0/caps.bend as C

def valid.ap(+s: C.CapState) -> {C.CapState.valid(s) == True{} : Bool} -> {C.CapSet.subset(C.CapState.ambient(s), C.CapState.permitted(s)) == True{} : Bool}:
  match s:
    case C.CapState{+p, +i, +e, +b, +a}:
      h => bool.and_l(C.CapSet.subset(a, p), C.CapSet.subset(a, i))(bool.and_r(C.CapSet.subset(e, p), Bool.and(C.CapSet.subset(a, p), C.CapSet.subset(a, i)))(h))

Uses (9):
  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=bool.and_l
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-caps@0.1.0.0/PROOF.bend&name=bool.and_r
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-caps@0.1.0.0/caps.bend&name=CapSet.subset
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-caps@0.1.0.0/caps.bend&name=CapState
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-caps@0.1.0.0/caps.bend&name=CapState.ambient
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-caps@0.1.0.0/caps.bend&name=CapState.permitted
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-caps@0.1.0.0/caps.bend&name=CapState.valid