PROOF.valid.intro: def of bend-osdev-caps@0.1.0.0
Import: import bend-osdev-caps@0.1.0.0/PROOF.bend as PROOF
Lines 81-84 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=81&end_line=84

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

def valid.intro(+s: C.CapState) -> {C.CapSet.subset(C.CapState.effective(s), C.CapState.permitted(s)) == True{} : Bool} -> {C.CapSet.subset(C.CapState.ambient(s), C.CapState.permitted(s)) == True{} : Bool} -> {C.CapSet.subset(C.CapState.ambient(s), C.CapState.inheritable(s)) == True{} : Bool} -> {C.CapState.valid(s) == True{} : Bool}:
  match s:
    case C.CapState{+p, +i, +e, +b, +a}:
      h1 => h2 => h3 => bool.and3(C.CapSet.subset(e, p), C.CapSet.subset(a, p), C.CapSet.subset(a, i))(h1)(h2)(h3)

Uses (9):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-caps@0.1.0.0/PROOF.bend&name=bool.and3
  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.effective
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-caps@0.1.0.0/caps.bend&name=CapState.inheritable
  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