LAWS.ambient_lower_rest_unchanged: law of bend-osdev-caps@0.1.0.0
Import: import bend-osdev-caps@0.1.0.0/LAWS.bend as LAWS
Lines 218-222 of bend-osdev-caps@0.1.0.0/LAWS.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-caps@0.1.0.0/LAWS.bend&start_line=218&end_line=222

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

law ambient_lower_rest_unchanged:
  for +k: C.CapsKernel
  for +c: C.CapCred
  for +x: U32
  {C.CapState.with_ambient(C.CapCred.sets(C.Caps.or(A.Caps.ambient_lower(k, c, x), c)), C.CapSet.empty()) == C.CapState.with_ambient(C.CapCred.sets(c), C.CapSet.empty()) : C.CapState}

Uses (11):
  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=al.rest
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-caps@0.1.0.0/adjust.bend&name=Caps.ambient_lower
  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.empty
  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.with_ambient
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-caps@0.1.0.0/caps.bend&name=Caps.or
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-caps@0.1.0.0/caps.bend&name=CapsKernel
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-caps@0.1.0.0/caps.bend&name=CapsKernel.valid