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Proof step 271 from proof inv-write_inode (previous step)

icache[m] = mkientry(boolvar, mkinode(m0, md0, boolvar0, m1, m3, m4)), afs-cons(dirs, files), afs-cons(dirs, files[m, (files[m].meta:= md).size:= m2]), synced(dirs, icache, pcache), m ∈ icache, m ∈ files ⊦ synced(dirs, icache[m0, mkientry(false, mkinode(m0, md, boolvar0, m1, m3, m2))], pcache)

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 272:
⊦ synced(dirs, icache, pcache) → (¬ synced(dirs0, icache0, pcache0) ↔ ¬(∀ ino. (ino ∈ dirs → synced(ino, icache, pcache)) → ino ∈ dirs0 → synced(ino, icache0, pcache0)))
Proof step 273:
icache[m] = mkientry(boolvar, mkinode(m0, md0, boolvar0, m1, m3, m4)), afs-cons(dirs, files[m, (files[m].meta:= md).size:= m2]), afs-cons(dirs, files), synced(dirs, icache, pcache), m ∈ files, m ∈ icache ⊦ ∀ ino. (ino ∈ dirs → synced(ino, icache, pcache)) → ino ∈ dirs → synced(ino, icache[m0, mkientry(false, mkinode(m0, md, boolvar0, m1, m3, m2))], pcache)

Rule argument

spec: cache-base name: synced-dirs-variant1 seq: ⊦ synced(dirs, icache, pcache) → ( ¬ synced(dirs0, icache0, pcache0) ↔ ¬ (∀ ino. (ino ∈ dirs → synced(ino, icache, pcache)) → ino ∈ dirs0 → synced(ino, icache0, pcache0))) subst: [dirs, icache, pcache, dirs0, icache0, pcache0] → [dirs, icache, pcache, dirs, icache [m0, mkientry(false, mkinode(m0, md, boolvar0, m1, m3, m2)) ], pcache] flags: <all paths>

Additional information

Used terms: dirs, icache, pcache, dirs, icache[m0, mkientry(false, mkinode(m0, md, boolvar0, m1, m3, m2))], pcache