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Proof step 127 from proof inv-mkdir (previous step)

(∅)[ino] = mkientry(true, inode), dirs0[m0] = mkdir(m3, md1, # links(m0, dirs0), m5, entries0), pcache[datakey(ino, n)] = mkpentry(boolvar, buf), afs-cons ((dirs0[m0, mkdir(m3 + 1, md1, # links(m0, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[ino0, mkdir(0, md, 1, 0, ∅)] [m0, mkdir(m3 + 1, md2, # links(m0, dirs0), m5 + 1, entries0[str, ino0]) ], files), afs-cons(dirs0, files), synced(dirs0, icache0, pcache), ino ∈ icache0[m0, mkientry(false, mkinode(m0, md2, true, # links(m0, dirs0), m5 + 1, m3 + 1))] [ino0, mkientry(false, mkinode(ino0, md, true, 1, 0, 0)) ], m0 ∈ dirs0, ino ∈ dirs0, datakey(ino, n) ∈ pcache → ¬ boolvar, asynced1 → synced(files, icache0, pcache), ∀ key. key ∈ pcache → key.data? ∧ # pcache[key].page = VFS_PAGE_SIZE ∧ key.ino ∈ files ∧ (¬ pcache[key].dirty → key.part ∈ files[key.ino].content ∧ pcache[key].page = files[key.ino].content[key.part]), ∀ n. datakey(ino, n) ∈ pcache → ¬ pcache[datakey(ino, n)].dirty, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ ino = m0, ino0 = 0, ino ∈ icache0, str ∈ entries0, ino0 ∈ files, ino0 ∈ dirs0

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 128:
⊦ ino ∈ icache[ino0, ie] ↔ ino = ino0 ∨ ino ∈ icache

Rule argument

spec: store, inst: icache name: In-insert seq: ⊦ ino ∈ icache[ino0, ie] ↔ ino = ino0 ∨ ino ∈ icache subst: [ino, icache, ino0, ie] → [ino, icache0 [m0, mkientry (false, mkinode (m0, md2, true, # links(m0, dirs0), m5 + 1, m3 + 1)) ], ino0, mkientry(false, mkinode(ino0, md, true, 1, 0, 0))] flags: <all paths>

Additional information

Used simplifier rules: ⊦ ino ≠ ino0 → (ino ∈ icache[ino0, ie] ↔ ino ∈ icache); (s) Used terms: ino, icache0 [m0, mkientry (false, mkinode(m0, md2, true, # links(m0, dirs0), m5 + 1, m3 + 1)) ], ino0, mkientry(false, mkinode(ino0, md, true, 1, 0, 0))