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Proof step 209 from proof inv-evict (previous step)

# links(m, dirs) = 0, files[key.ino] = mkfile(m1, md0, m2, content0), files[m] = mkfile(m0, md, 0, content), evict(m, pcache)[key] = mkpentry(boolvar, buf), pcache[key] = mkpentry(boolvar0, buf0), afs-cons(dirs, files), afs-cons(dirs, files -- m), synced(dirs, icache, pcache), m ∈ files, key ∈ evict(m, pcache), key ∈ pcache → key.data? ∧ # buf0 = VFS_PAGE_SIZE ∧ key.ino ∈ files ∧ (¬ boolvar0 → key.part ∈ content0 ∧ buf0 = content0[key.part]), asynced1 → synced(files, icache, pcache), key ∈ pcache → key.data?, ∀ 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. key ∈ evict(m, pcache) → key.data? ∧ key.ino ≠ m, ∀ key. key ∈ pcache → key.data? ⊦ m = ROOT_INO, m ∈ dirs, key.data? ∧ # buf = VFS_PAGE_SIZE ∧ key.ino ≠ m ∧ key.ino ∈ files ∧ (¬ boolvar → key.part ∈ content0 ∧ buf = content0[key.part])

User applied rule all left

And obtained the following new goals

Proof step 210:
# links(m, dirs) = 0, pcache[key] = mkpentry(boolvar0, buf0), evict(m, pcache)[key] = mkpentry(boolvar, buf), files[m] = mkfile(m0, md, 0, content), files[key.ino] = mkfile(m1, md0, m2, content0), afs-cons(dirs, files -- m), afs-cons(dirs, files), synced(dirs, icache, pcache), key ∈ evict(m, pcache), m ∈ files, key ∈ pcache → key.data?, asynced1 → synced(files, icache, pcache), key ∈ pcache → key.data? ∧ # buf0 = VFS_PAGE_SIZE ∧ key.ino ∈ files ∧ (¬ boolvar0 → key.part ∈ content0 ∧ buf0 = content0[key.part]), key ∈ evict(m, pcache) → key.data? ∧ key.ino ≠ m, ∀ key. key ∈ pcache → key.data?, ∀ key. key ∈ evict(m, pcache) → key.data? ∧ key.ino ≠ m, ∀ 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]) ⊦ m = ROOT_INO, m ∈ dirs, key.data? ∧ # buf = VFS_PAGE_SIZE ∧ key.ino ≠ m ∧ key.ino ∈ files ∧ (¬ boolvar → key.part ∈ content0 ∧ buf = content0[key.part])

Rule argument

pos: left 15 terms: key abort: F discard: F computed: T

Additional information

Used terms: key