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

pcache[key] = mkpentry(boolvar1, buf), icache[m] = mkientry(boolvar, mkinode(m1, md1, boolvar0, m3, m4, m5)), dirs[m] = mkdir(m0, md0, # links(m, dirs), m2, entries), files[key.ino] = mkfile(m6, md2, m7, content), afs-cons(dirs[m, mkdir(m0, md, # links(m, dirs), m2, entries)], files), afs-cons(dirs, files), synced(dirs, icache, pcache), key ∈ pcache, m ∈ icache, m ∈ dirs, asynced2 → synced(files, icache, pcache), ∀ key0. key0 ∈ pcache → key0.data? ∧ # pcache[key0].page = VFS_PAGE_SIZE ∧ key0.ino ∈ files ∧ (¬ pcache[key0].dirty → key0.part ∈ files[key0.ino].content ∧ pcache[key0].page = files[key0.ino].content[key0.part]) ⊦ key.data? ∧ # buf = VFS_PAGE_SIZE ∧ key.ino ∈ files ∧ (¬ boolvar1 → key.part ∈ content ∧ buf = content[key.part])

Heuristic use patterns applied rule all left

And closed the goal!

Rule argument

pos: left 12 terms: key abort: T discard: F computed: F

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%⊦ ino ∈ dirs ∧ dirs[ino] = mkdir(m0, md0, n1, n2, entries) → links(ino0, dirs[ino, mkdir(m, md, n, n0, entries)]) = links(ino0, dirs); (s)% ⊦ mkpentry(boolvar, buf).page = buf; (s)% ⊦ mkpentry(boolvar, buf).dirty ↔ boolvar; (s)% ⊦ mkfile(m, md, m0, content).content = content; (s) Used terms: key