PROOF.cs.p.r1: def of bend-osdev-caps@0.1.0.0
Import: import bend-osdev-caps@0.1.0.0/PROOF.bend as PROOF
Lines 841-846 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=841&end_line=846

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 cs.p.r1(+ok: Bool, +c: C.CapCred, +e: C.CapSet(), +p: C.CapSet(), +i: C.CapSet()) -> {C.CapSet.subset(p, C.CapState.permitted(C.CapCred.sets(c))) == ok : Bool} -> {C.CapSet.subset(C.CapState.permitted(C.CapCred.sets(C.Caps.or(A.CapAdjust.capset.r1(ok, c, e, p, i), c))), C.CapState.permitted(C.CapCred.sets(c))) == True{} : Bool}:
  match ok:
    case False{}:
      h => set.sub_refl(C.CapState.permitted(C.CapCred.sets(c)))
    case True{}:
      h => cs.p.r2(C.CapSet.subset(e, p), c, e, p, i)(h)

Uses (10):
  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=cs.p.r2
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-caps@0.1.0.0/PROOF.bend&name=set.sub_refl
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-caps@0.1.0.0/adjust.bend&name=CapAdjust.capset.r1
  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
  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.permitted
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-caps@0.1.0.0/caps.bend&name=Caps.or