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Proof step 451 from proof inv-rename-file-dentry (previous step)

dirs0[m3] = mkdir(m1, md1, # links(m3, dirs0), m4, entries), files[entries[str0]] = mkfile(m0, md0, # links(entries[str0], dirs0), content), afs-cons(dirs0, files), afs-cons (dirs0[m3, mkdir(m1, md2, # links(m3, dirs0), m4, entries)], files[entries[str0], mkfile(m, md3, # links(entries[str0], dirs0), content)]), synced(dirs0, icache0, pcache), m3 ∈ dirs0, str0 ∈ entries, entries[str0] ∈ files, asynced2 → synced(files, icache0, pcache), links(m3, dirs0) ≠ ∅ ∨ m3 = ROOT_INO ⊦ synced (dirs0[m3, mkdir(m1, md2, # links(m3, dirs0), m4, entries)], icache0[m3, mkientry(false, mkinode(m3, md2, true, # links(m3, dirs0), m4, m1))] [entries[str0], mkientry(false, mkinode(entries[str0], md3, false, # links(entries[str0], dirs0), 0, m)) ], pcache), entries[str0] ∈ dirs0

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 452:
⊦ synced(dirs, icache, pcache) → (¬ synced(dirs0, icache0, pcache0) ↔ ¬(∀ ino. (ino ∈ dirs → synced(ino, icache, pcache)) → ino ∈ dirs0 → synced(ino, icache0, pcache0)))
Proof step 453:
files[entries[str0]] = mkfile(m0, md0, # links(entries[str0], dirs0), content), dirs0[m3] = mkdir(m1, md1, # links(m3, dirs0), m4, entries), afs-cons (dirs0[m3, mkdir(m1, md2, # links(m3, dirs0), m4, entries)], files[entries[str0], mkfile(m, md3, # links(entries[str0], dirs0), content)]), afs-cons(dirs0, files), synced(dirs0, icache0, pcache), entries[str0] ∈ files, str0 ∈ entries, m3 ∈ dirs0, asynced2 → synced(files, icache0, pcache), links(m3, dirs0) ≠ ∅ ∨ m3 = ROOT_INO ⊦ entries[str0] ∈ dirs0, ∀ ino. (ino ∈ dirs0 → synced(ino, icache0, pcache)) → ino ∈ dirs0[m3, mkdir(m1, md2, # links(m3, dirs0), m4, entries)] → synced (ino, icache0[m3, mkientry(false, mkinode(m3, md2, true, # links(m3, dirs0), m4, m1))] [entries[str0], mkientry(false, mkinode(entries[str0], md3, false, # links(entries[str0], dirs0), 0, m)) ], 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] → [dirs0, icache0, pcache, dirs0 [m3, mkdir(m1, md2, # links(m3, dirs0), m4, entries) ], icache0 [m3, mkientry (false, mkinode(m3, md2, true, # links(m3, dirs0), m4, m1)) ] [entries[str0], mkientry (false, mkinode (entries[str0], md3, false, # links(entries[str0], dirs0), 0, m)) ], pcache] flags: <all paths>

Additional information

Used terms: dirs0, icache0, pcache, dirs0[m3, mkdir(m1, md2, # links(m3, dirs0), m4, entries)], icache0 [m3, mkientry(false, mkinode(m3, md2, true, # links(m3, dirs0), m4, m1)) ] [entries[str0], mkientry (false, mkinode (entries[str0], md3, false, # links(entries[str0], dirs0), 0, m)) ], pcache