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Proof step 126 from proof inv-create (previous step)

(key.ino = ino0 ⊃ mkfile(0, md, 1, ∅);(files0 ++ ino0)[key.ino]) = mkfile(m, md0, m2, content), pcache[key] = mkpentry(boolvar, buf), dirs0[m1] = mkdir(m0, md2, # links(m1, dirs0), m4, entries1), afs-cons(dirs0[m1, mkdir(m0 + 1, md1, # links(m1, dirs0), m4, entries1[str, ino0])], (files0 ++ ino0)[ino0, mkfile(0, md, 1, ∅)]), afs-cons(dirs0, files0), synced(dirs0, icache0, pcache), key ∈ pcache, m1 ∈ dirs0, 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, str ∈ entries1, ino0 ∈ files0, ino0 ∈ dirs0, key.data? ∧ # buf = VFS_PAGE_SIZE ∧ (key.ino = ino0 ∨ key.ino ∈ files0) ∧ (¬ boolvar → key.part ∈ content ∧ buf = content[key.part])

Heuristic use patterns applied rule all left

And obtained the following new goals

Proof step 127:
(key.ino = ino0 ⊃ mkfile(0, md, 1, ∅);(files0 ++ ino0)[key.ino]) = mkfile(m, md0, m2, content), dirs0[m1] = mkdir(m0, md2, # links(m1, dirs0), m4, entries1), pcache[key] = 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(dirs0, icache0, pcache), m1 ∈ dirs0, key ∈ pcache, asynced1 → synced(files0, icache0, pcache), 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]), ∀ 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, key.data? ∧ # buf = VFS_PAGE_SIZE ∧ (key.ino = ino0 ∨ key.ino ∈ files0) ∧ (¬ boolvar → key.part ∈ content ∧ buf = content[key.part])

Rule argument

pos: left 10 terms: key abort: T discard: F computed: F

Additional information

Used terms: key