PROOF.cap.gapp: def of bend-osdev-apparmor@0.1.0.0
Import: import bend-osdev-apparmor@0.1.0.0/PROOF.bend as PROOF
Lines 3567-3568 of bend-osdev-apparmor@0.1.0.0/PROOF.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-apparmor@0.1.0.0/PROOF.bend&start_line=3567&end_line=3568

import Base
import bend-osdev-apparmor@0.1.0.0/perm.bend as P
import bend-osdev-apparmor@0.1.0.0/rule_capability.bend as RC

def cap.gapp(+xs: List<&2, RC.AaCapRule>, +ys: List<&2, RC.AaCapRule>, +q: RC.AaCapQuery) -> {RC.AaCapRule.grants(RC.AaCapRule.append(xs, ys), q) == P.AaGrant.append(RC.AaCapRule.grants(xs, q), RC.AaCapRule.grants(ys, q)) : List<&2, P.AaGrant>}:
  Equal.trans(List<&2, P.AaGrant>, RC.AaCapRule.grants.of(RC.AaCapRule.matching(RC.AaCapRule.append(xs, ys), q)), RC.AaCapRule.grants.of(RC.AaCapRule.append(RC.AaCapRule.matching(xs, q), RC.AaCapRule.matching(ys, q))), P.AaGrant.append(RC.AaCapRule.grants(xs, q), RC.AaCapRule.grants(ys, q)), Equal.cong(List<&2, RC.AaCapRule>, List<&2, P.AaGrant>, x => RC.AaCapRule.grants.of(x), RC.AaCapRule.matching(RC.AaCapRule.append(xs, ys), q), RC.AaCapRule.append(RC.AaCapRule.matching(xs, q), RC.AaCapRule.matching(ys, q)), cap.match_app(xs, ys, q)), cap.gof_app(RC.AaCapRule.matching(xs, q), RC.AaCapRule.matching(ys, q)))

Uses (13):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.cong
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.trans
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-apparmor@0.1.0.0/PROOF.bend&name=cap.gof_app
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-apparmor@0.1.0.0/PROOF.bend&name=cap.match_app
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-apparmor@0.1.0.0/perm.bend&name=AaGrant
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-apparmor@0.1.0.0/perm.bend&name=AaGrant.append
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-apparmor@0.1.0.0/rule_capability.bend&name=AaCapQuery
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-apparmor@0.1.0.0/rule_capability.bend&name=AaCapRule
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-apparmor@0.1.0.0/rule_capability.bend&name=AaCapRule.append
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-apparmor@0.1.0.0/rule_capability.bend&name=AaCapRule.grants
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-apparmor@0.1.0.0/rule_capability.bend&name=AaCapRule.grants.of
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-apparmor@0.1.0.0/rule_capability.bend&name=AaCapRule.matching