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Proof step 83 from proof inv-create (previous step)

icache0[m1, mkientry(false, mkinode(m1, md1, true, # links(m1, dirs0), m4, m0 + 1))][ino0, mkientry(false, mkinode(ino0, md, false, 1, 0, 0))] [ino ] = mkientry(boolvar1, inode0), pcache[datakey(ino, n)] = mkpentry(boolvar, buf), dirs0[m1] = mkdir(m0, md2, # links(m1, dirs0), m4, entries1), icache0[ino] = mkientry(boolvar0, inode), ino = ino0, 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(files0, icache0, pcache), m1 ∈ dirs0, ino ∈ files0 → (ino ∈ icache0 → ¬ boolvar0) ∧ (∀ n. datakey(ino, n) ∈ pcache → ¬ pcache[datakey(ino, n)].dirty), ∀ key. 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]), links(m1, dirs0) ≠ ∅ ∨ m1 = ROOT_INO, ino = ino0 ∨ ino ∈ files0 ⊦ ino0 = 0, str ∈ entries1, ino0 ∈ files0, ino0 ∈ dirs0, ( ino ∈ icache0[m1, mkientry(false, mkinode(m1, md1, true, # links(m1, dirs0), m4, m0 + 1))] [ino0, mkientry(false, mkinode(ino0, md, false, 1, 0, 0)) ] → ¬ boolvar1) ∧ (datakey(ino, n) ∈ pcache → ¬ boolvar)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 84:
pcache[datakey(ino0, n)] = mkpentry(true, buf), dirs0[m1] = mkdir(m0, md2, # links(m1, dirs0), m4, entries1), icache0[ino0] = mkientry(boolvar0, inode), 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(files0, icache0, pcache), datakey(ino0, n) ∈ pcache, m1 ∈ dirs0, ∀ key. 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]), links(m1, dirs0) ≠ ∅ ∨ m1 = ROOT_INO ⊦ ino0 = 0, str ∈ entries1, ino0 ∈ files0, ino0 ∈ dirs0

Rule argument

Additional information

Used simplifier rules: ⊦ ino ∈ icache[ino, ie]; (s)%⊦ mkientry(boolvar, inode) = mkientry(boolvar0, inode0) ↔ (boolvar ↔ boolvar0) ∧ inode = inode0; (ws)% ⊦ icache[ino, ie][ino] = ie; (s)