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Proof step 132 from proof inv-create (previous step)

(files0 ++ ino0)[m3] = mkfile(m, md0, m2, content), dirs0[m1] = mkdir(m0, md2, # links(m1, dirs0), m4, entries1), pcache[datakey(m3, m5)] = mkpentry(false, content0[m5]), files0[m3] = mkfile(m6, md3, # links(m3, dirs0), content0), 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), m3 ∈ files0, m1 ∈ dirs0, datakey(m3, m5) ∈ pcache, m5 ∈ content0, asynced1 → synced(files0, icache0, pcache), ∀ key0. key0 ∈ pcache → key0.data? ∧ # pcache[key0].page = VFS_PAGE_SIZE ∧ key0.ino ∈ files0 ∧ (¬ pcache[key0].dirty → key0.part ∈ files0[key0.ino].content ∧ pcache[key0].page = files0[key0.ino].content[key0.part]), links(m1, dirs0) ≠ ∅ ∨ m1 = ROOT_INO ⊦ ino0 = 0, ino0 ∈ dirs0, ino0 ∈ files0, str ∈ entries1, m5 ∈ content ∧ content0[m5] = content[m5]

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: heap, inst: file-heap name: at-alloc seq: ino ∈ files, ino0 ≠ 0, ¬ ino0 ∈ files ⊦ ino ≠ ino0 → (files ++ ino0)[ino] = files[ino] subst: [ino, files, ino0] → [m3, files0, ino0] flags: <all paths>

Additional information

Used simplifier rules: afs-cons-file-nlink: ⊦ afs-cons(dirs, files) ∧ ino ∈ files ∧ files[ino] = mkfile(m, md, n, content) → # links(ino, dirs) = n; (forward) from specification afs-base%⊦ mkfile(m, md, m0, content) = mkfile(m1, md0, m2, content0) ↔ m = m1 ∧ md = md0 ∧ m0 = m2 ∧ content = content0; (ws) Used terms: m3, files0, ino0