PROOF.net.inc: def of bend-osdev-apparmor@0.1.0.0
Import: import bend-osdev-apparmor@0.1.0.0/PROOF.bend as PROOF
Lines 3613-3614 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=3613&end_line=3614

import Base
import bend-osdev-apparmor@0.1.0.0/perm.bend as P
import bend-osdev-apparmor@0.1.0.0/options.bend as O
import bend-osdev-apparmor@0.1.0.0/profile.bend as PR
import bend-osdev-apparmor@0.1.0.0/eval.bend as V
import bend-osdev-apparmor@0.1.0.0/rule_network.bend as RN

def net.inc(+opts: O.AaOptions, +flags: PR.AaFlags, +req: P.AaPerms, +xs: List<&2, RN.AaNetRule>, +ys: List<&2, RN.AaNetRule>, +q: RN.AaNetQuery) -> {V.AaEval.decide(opts, flags, req, RN.AaNetRule.grants(RN.AaNetRule.append(RN.AaNetRule.append(xs, ys), ys), q)) == V.AaEval.decide(opts, flags, req, RN.AaNetRule.grants(RN.AaNetRule.append(xs, ys), q)) : V.AaDecision}:
  Equal.trans(V.AaDecision, V.AaEval.decide(opts, flags, req, RN.AaNetRule.grants(RN.AaNetRule.append(RN.AaNetRule.append(xs, ys), ys), q)), V.AaEval.decide(opts, flags, req, P.AaGrant.append(P.AaGrant.append(RN.AaNetRule.grants(xs, q), RN.AaNetRule.grants(ys, q)), RN.AaNetRule.grants(ys, q))), V.AaEval.decide(opts, flags, req, RN.AaNetRule.grants(RN.AaNetRule.append(xs, ys), q)), Equal.cong(List<&2, P.AaGrant>, V.AaDecision, x => V.AaEval.decide(opts, flags, req, x), RN.AaNetRule.grants(RN.AaNetRule.append(RN.AaNetRule.append(xs, ys), ys), q), P.AaGrant.append(P.AaGrant.append(RN.AaNetRule.grants(xs, q), RN.AaNetRule.grants(ys, q)), RN.AaNetRule.grants(ys, q)), Equal.trans(List<&2, P.AaGrant>, RN.AaNetRule.grants(RN.AaNetRule.append(RN.AaNetRule.append(xs, ys), ys), q), P.AaGrant.append(RN.AaNetRule.grants(RN.AaNetRule.append(xs, ys), q), RN.AaNetRule.grants(ys, q)), P.AaGrant.append(P.AaGrant.append(RN.AaNetRule.grants(xs, q), RN.AaNetRule.grants(ys, q)), RN.AaNetRule.grants(ys, q)), net.gapp(RN.AaNetRule.append(xs, ys), ys, q), Equal.cong(List<&2, P.AaGrant>, List<&2, P.AaGrant>, x => P.AaGrant.append(x, RN.AaNetRule.grants(ys, q)), RN.AaNetRule.grants(RN.AaNetRule.append(xs, ys), q), P.AaGrant.append(RN.AaNetRule.grants(xs, q), RN.AaNetRule.grants(ys, q)), net.gapp(xs, ys, q)))), Equal.trans(V.AaDecision, V.AaEval.decide(opts, flags, req, P.AaGrant.append(P.AaGrant.append(RN.AaNetRule.grants(xs, q), RN.AaNetRule.grants(ys, q)), RN.AaNetRule.grants(ys, q))), V.AaEval.decide(opts, flags, req, P.AaGrant.append(RN.AaNetRule.grants(xs, q), RN.AaNetRule.grants(ys, q))), V.AaEval.decide(opts, flags, req, RN.AaNetRule.grants(RN.AaNetRule.append(xs, ys), q)), inc.decide(opts, flags, req, RN.AaNetRule.grants(xs, q), RN.AaNetRule.grants(ys, q)), Equal.cong(List<&2, P.AaGrant>, V.AaDecision, x => V.AaEval.decide(opts, flags, req, x), P.AaGrant.append(RN.AaNetRule.grants(xs, q), RN.AaNetRule.grants(ys, q)), RN.AaNetRule.grants(RN.AaNetRule.append(xs, ys), q), Equal.sym(List<&2, P.AaGrant>, RN.AaNetRule.grants(RN.AaNetRule.append(xs, ys), q), P.AaGrant.append(RN.AaNetRule.grants(xs, q), RN.AaNetRule.grants(ys, q)), net.gapp(xs, ys, q)))))

Uses (17):
  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.sym
  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=inc.decide
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-apparmor@0.1.0.0/PROOF.bend&name=net.gapp
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-apparmor@0.1.0.0/eval.bend&name=AaDecision
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-apparmor@0.1.0.0/eval.bend&name=AaEval.decide
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-apparmor@0.1.0.0/options.bend&name=AaOptions
  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/perm.bend&name=AaPerms
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-apparmor@0.1.0.0/profile.bend&name=AaFlags
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-apparmor@0.1.0.0/rule_network.bend&name=AaNetQuery
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-apparmor@0.1.0.0/rule_network.bend&name=AaNetRule
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-apparmor@0.1.0.0/rule_network.bend&name=AaNetRule.append
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-apparmor@0.1.0.0/rule_network.bend&name=AaNetRule.grants