PROOF.ar.valid: def of bend-osdev-caps@0.1.0.0
Import: import bend-osdev-caps@0.1.0.0/PROOF.bend as PROOF
Lines 937-946 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=937&end_line=946

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

def ar.valid(+v: Bool, +lk: Bool, +al: Bool, +c: C.CapCred, +x: U32) -> {A.CapAdjust.ambient.allowed(c, x) == al : Bool} -> {C.CapState.valid(C.CapCred.sets(c)) == True{} : Bool} -> {C.CapState.valid(C.CapCred.sets(C.Caps.or(A.CapAdjust.ambient_raise.go(v, lk, al, c, x), c))) == True{} : Bool}:
  match v lk al c:
    case False{} lk al c:
      h => hv => hv
    case True{} True{} al c:
      h => hv => hv
    case True{} False{} False{} c:
      h => hv => hv
    case True{} False{} True{} C.CapCred{r, eu, sv, nr, na, C.CapState{+p, +i, +e, +b, +a}}:
      +h => +hv => bool.and3(C.CapSet.subset(e, p), C.CapSet.subset(C.CapSet.union(a, C.CapSet.of(x)), p), C.CapSet.subset(C.CapSet.union(a, C.CapSet.of(x)), i))(valid.ep(C.CapState{p, i, e, b, a})(hv))(set.lub(a, C.CapSet.of(x), p)(valid.ap(C.CapState{p, i, e, b, a})(hv))(caps.has_of(C.Cap.valid(x), p, x)(bool.and_l(C.CapSet.has(p, x), C.CapSet.has(i, x))(h))))(set.lub(a, C.CapSet.of(x), i)(valid.ai(C.CapState{p, i, e, b, a})(hv))(caps.has_of(C.Cap.valid(x), i, x)(bool.and_r(C.CapSet.has(p, x), C.CapSet.has(i, x))(h))))

Uses (22):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  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/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/PROOF.bend&name=caps.has_of
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-caps@0.1.0.0/PROOF.bend&name=set.lub
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-caps@0.1.0.0/PROOF.bend&name=valid.ai
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-caps@0.1.0.0/PROOF.bend&name=valid.ap
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-caps@0.1.0.0/PROOF.bend&name=valid.ep
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-caps@0.1.0.0/adjust.bend&name=CapAdjust.ambient.allowed
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-caps@0.1.0.0/adjust.bend&name=CapAdjust.ambient_raise.go
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-caps@0.1.0.0/caps.bend&name=Cap.valid
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-caps@0.1.0.0/caps.bend&name=CapCred
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-caps@0.1.0.0/caps.bend&name=CapCred.sets
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-caps@0.1.0.0/caps.bend&name=CapSet.has
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-caps@0.1.0.0/caps.bend&name=CapSet.of
  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=CapSet.union
  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.valid
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-caps@0.1.0.0/caps.bend&name=Caps.or