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Proof step 86 from proof inv-writepage (previous step)

# buf = VFS_PAGE_SIZE, (key.ino = m ⊃ mkfile(m0, md, # links(key.ino, dirs), content[pageno, buf]);files[key.ino]) = mkfile(m1, md0, m2, content0), pcache[key] = mkpentry(boolvar, buf0), files[m] = mkfile(m0, md, # links(m, dirs), content), afs-cons(dirs, files[m, mkfile(m0, md, # links(m, dirs), content[pageno, buf])]), afs-cons(dirs, files), synced(files, icache, pcache), synced(dirs, icache, pcache), key ∈ pcache, m ∈ files, ∀ key. key ∈ pcache → key.data? ∧ # pcache[key].page = VFS_PAGE_SIZE ∧ valid-file-ino(key.ino, dirs, files) ∧ (¬ pcache[key].dirty → key.part ∈ files[key.ino].content ∧ pcache[key].page = files[key.ino].content[key.part]) ⊦ key = datakey(m, pageno), key.data? ∧ # buf0 = VFS_PAGE_SIZE ∧ key.ino ∈ files ∧ (¬ boolvar → key.part ∈ content0 ∧ buf0 = content0[key.part])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 87:
# buf = VFS_PAGE_SIZE, (key.ino = m ⊃ mkfile(m0, md, # links(key.ino, dirs), content[pageno, buf]);files[key.ino]) = mkfile(m1, md0, m2, content0), files[m] = mkfile(m0, md, # links(m, dirs), content), pcache[key] = mkpentry(boolvar, buf0), afs-cons(dirs, files), afs-cons(dirs, files[m, mkfile(m0, md, # links(m, dirs), content[pageno, buf])]), synced(dirs, icache, pcache), synced(files, icache, pcache), m ∈ files, key ∈ 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 = datakey(m, pageno), key.data? ∧ # buf0 = VFS_PAGE_SIZE ∧ key.ino ∈ files ∧ (¬ boolvar → key.part ∈ content0 ∧ buf0 = content0[key.part])

Rule argument

Additional information

Used simplifier rules: ⊦ valid-file-ino(ino, dirs, files) ↔ ino ∈ files; (s)