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Proof step 123 from proof inv-unlink (previous step)

# links(entries0[str], dirs0) = m2 + 1, dirs0[m0] = mkdir(m8 + 1, md2, # links(m0, dirs0), m7, entries0), files0[entries0[str]] = mkfile(m1, md1, m2 + 1, content0), afs-cons(dirs0, files0), afs-cons(dirs0[m0, mkdir(m8, md3, # links(m0, dirs0), m7, entries0 -- str)], files0[entries0[str], mkfile(m3, md0, m2, content0)]), synced(dirs0, icache0, pcache), str ∈ entries0, entries0[str] ∈ files0, m0 ∈ dirs0, asynced1 → synced(files0, icache0, pcache), links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ synced (dirs0[m0, mkdir(m8, md3, # links(m0, dirs0), m7, entries0 -- str)], icache0[entries0[str], mkientry(false, mkinode(entries0[str], md0, false, m2, 0, m3))] [m0, mkientry(false, mkinode(m0, md3, true, # links(m0, dirs0), m7, m8)) ], pcache)

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 124:
⊦ synced(dirs, icache, pcache) → (¬ synced(dirs0, icache0, pcache0) ↔ ¬(∀ ino. (ino ∈ dirs → synced(ino, icache, pcache)) → ino ∈ dirs0 → synced(ino, icache0, pcache0)))
Proof step 125:
# links(entries0[str], dirs0) = m2 + 1, files0[entries0[str]] = mkfile(m1, md1, m2 + 1, content0), dirs0[m0] = mkdir(m8 + 1, md2, # links(m0, dirs0), m7, entries0), afs-cons(dirs0[m0, mkdir(m8, md3, # links(m0, dirs0), m7, entries0 -- str)], files0[entries0[str], mkfile(m3, md0, m2, content0)]), afs-cons(dirs0, files0), synced(dirs0, icache0, pcache), m0 ∈ dirs0, entries0[str] ∈ files0, str ∈ entries0, asynced1 → synced(files0, icache0, pcache), links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ ∀ ino. (ino ∈ dirs0 → synced(ino, icache0, pcache)) → ino ∈ dirs0[m0, mkdir(m8, md3, # links(m0, dirs0), m7, entries0 -- str)] → synced (ino, icache0[entries0[str], mkientry(false, mkinode(entries0[str], md0, false, m2, 0, m3))] [m0, mkientry(false, mkinode(m0, md3, true, # links(m0, dirs0), m7, m8)) ], 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 [m0, mkdir(m8, md3, # links(m0, dirs0), m7, entries0 -- str) ], icache0 [entries0[str], mkientry (false, mkinode(entries0[str], md0, false, m2, 0, m3)) ] [m0, mkientry (false, mkinode(m0, md3, true, # links(m0, dirs0), m7, m8)) ], pcache] flags: <all paths>

Additional information

Used terms: dirs0, icache0, pcache, dirs0[m0, mkdir(m8, md3, # links(m0, dirs0), m7, entries0 -- str)], icache0 [entries0[str], mkientry(false, mkinode(entries0[str], md0, false, m2, 0, m3)) ] [m0, mkientry(false, mkinode(m0, md3, true, # links(m0, dirs0), m7, m8)) ], pcache