LAWS.ambient_lower_valid: law of bend-osdev-caps@0.1.0.0
Import: import bend-osdev-caps@0.1.0.0/LAWS.bend as LAWS
Lines 205-210 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=205&end_line=210

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_valid:
  for +k: C.CapsKernel
  for +c: C.CapCred
  for +x: U32
  for h: {C.CapState.valid(C.CapCred.sets(c)) == True{} : Bool}
  {C.CapState.valid(C.CapCred.sets(C.Caps.or(A.Caps.ambient_lower(k, c, x), c))) == True{} : Bool}

Uses (10):
  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=al.valid
  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=CapState.valid
  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