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Proof step 90 from proof inv-create (previous step)

(∅)[ino] = mkientry(true, inode), dirs0[m1] = mkdir(m0, md2, # links(m1, dirs0), m4, entries1), pcache[datakey(ino, n)] = mkpentry(boolvar, buf), 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(files0, icache0, pcache), 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))], m1 ∈ dirs0, ino ∈ files0, datakey(ino, n) ∈ pcache → ¬ boolvar, ∀ key. key ∈ pcache → key.data? ∧ # pcache[key].page = VFS_PAGE_SIZE ∧ key.ino ∈ files0 ∧ (¬ pcache[key].dirty → key.part ∈ files0[key.ino].content ∧ pcache[key].page = files0[key.ino].content[key.part]), ∀ n. datakey(ino, n) ∈ pcache → ¬ pcache[datakey(ino, n)].dirty, links(m1, dirs0) ≠ ∅ ∨ m1 = ROOT_INO ⊦ ino = m1, ino0 = 0, ino ∈ icache0, ino0 ∈ dirs0, ino0 ∈ files0, str ∈ entries1

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 91:
⊦ 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 [m1, mkientry (false, mkinode(m1, md1, true, # links(m1, dirs0), m4, m0 + 1)) ], ino0, mkientry(false, mkinode(ino0, md, false, 1, 0, 0))] flags: <all paths>

Additional information

Used simplifier rules: ⊦ ino ≠ ino0 → (ino ∈ icache[ino0, ie] ↔ ino ∈ icache); (s) Used terms: 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))