PROOF.al.valid: def of bend-osdev-caps@0.1.0.0
Import: import bend-osdev-caps@0.1.0.0/PROOF.bend as PROOF
Lines 948-953 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=948&end_line=953

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 al.valid(+v: Bool, +c: C.CapCred, +x: U32) -> {C.CapState.valid(C.CapCred.sets(c)) == True{} : Bool} -> {C.CapState.valid(C.CapCred.sets(C.Caps.or(A.CapAdjust.ambient_lower.go(v, c, x), c))) == True{} : Bool}:
  match v c:
    case False{} c:
      hv => hv
    case True{} C.CapCred{r, eu, sv, nr, na, C.CapState{+p, +i, +e, +b, +a}}:
      +hv => bool.and3(C.CapSet.subset(e, p), C.CapSet.subset(C.CapSet.minus(a, C.CapSet.of(x)), p), C.CapSet.subset(C.CapSet.minus(a, C.CapSet.of(x)), i))(valid.ep(C.CapState{p, i, e, b, a})(hv))(set.minus_within(a, C.CapSet.of(x), p)(valid.ap(C.CapState{p, i, e, b, a})(hv)))(set.minus_within(a, C.CapSet.of(x), i)(valid.ai(C.CapState{p, i, e, b, a})(hv)))

Uses (16):
  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=set.minus_within
  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_lower.go
  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.minus
  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=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