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Proof step 99 from proof inv-create (previous step)

dirs0[m1] = mkdir(m0, md2, # links(m1, dirs0), m4, entries1), afs-cons(dirs0[m1, mkdir(m0 + 1, md1, # links(m1, dirs0), m4, entries1[str, ino0])], (files0 ++ ino0)[ino0, mkfile(0, md, 1, ∅)]), afs-cons(dirs0, files0), synced(dirs0, icache0, pcache), m1 ∈ dirs0, asynced1 → synced(files0, icache0, pcache), links(m1, dirs0) ≠ ∅ ∨ m1 = ROOT_INO ⊦ ino0 = 0, synced (dirs0[m1, mkdir(m0 + 1, md1, # links(m1, dirs0), m4, entries1[str, ino0])], icache0[m1, mkientry(false, mkinode(m1, md1, true, # links(m1, dirs0), m4, m0 + 1))][ino0, mkientry(false, mkinode(ino0, md, false, 1, 0, 0))], pcache), str ∈ entries1, ino0 ∈ files0, ino0 ∈ dirs0

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 100:
⊦ synced(dirs, icache, pcache) → (¬ synced(dirs0, icache0, pcache0) ↔ ¬(∀ ino. (ino ∈ dirs → synced(ino, icache, pcache)) → ino ∈ dirs0 → synced(ino, icache0, pcache0)))
Proof step 101:
dirs0[m1] = mkdir(m0, md2, # links(m1, dirs0), m4, entries1), afs-cons(dirs0, files0), afs-cons(dirs0[m1, mkdir(m0 + 1, md1, # links(m1, dirs0), m4, entries1[str, ino0])], (files0 ++ ino0)[ino0, mkfile(0, md, 1, ∅)]), synced(dirs0, icache0, pcache), m1 ∈ dirs0, asynced1 → synced(files0, icache0, pcache), links(m1, dirs0) ≠ ∅ ∨ m1 = ROOT_INO ⊦ ino0 = 0, ino0 ∈ dirs0, ino0 ∈ files0, str ∈ entries1, ∀ ino. (ino ∈ dirs0 → synced(ino, icache0, pcache)) → ino ∈ dirs0[m1, mkdir(m0 + 1, md1, # links(m1, dirs0), m4, entries1[str, ino0])] → synced (ino, icache0[m1, mkientry(false, mkinode(m1, md1, true, # links(m1, dirs0), m4, m0 + 1))] [ino0, mkientry(false, mkinode(ino0, md, false, 1, 0, 0)) ], 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 [m1, mkdir (m0 + 1, md1, # links(m1, dirs0), m4, entries1[str, ino0]) ], icache0 [m1, mkientry (false, mkinode(m1, md1, true, # links(m1, dirs0), m4, m0 + 1)) ] [ino0, mkientry(false, mkinode(ino0, md, false, 1, 0, 0)) ], pcache] flags: <all paths>

Additional information

Used terms: dirs0, icache0, pcache, dirs0 [m1, mkdir(m0 + 1, md1, # links(m1, dirs0), m4, entries1[str, ino0]) ], icache0 [m1, mkientry (false, mkinode(m1, md1, true, # links(m1, dirs0), m4, m0 + 1)) ] [ino0, mkientry(false, mkinode(ino0, md, false, 1, 0, 0)) ], pcache