[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 358 from proof inv-truncate-buff-none-cached (previous step)

# buf0 = VFS_PAGE_SIZE, pcache0[datakey(m0, m2 / VFS_PAGE_SIZE)] = mkpentry(boolvar, buf0), files0[m0] = mkfile(m1, md1, # links(m0, dirs), content0), key.data?, afs-cons(dirs, files0), afs-cons(dirs, files0[m0, mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2))]), pcache-cons(pcache0, dirs, files0), synced(dirs, icache, pcache0), datakey(m0, m2 / VFS_PAGE_SIZE) ∈ pcache0, m0 ∈ files0, key ∈ pcache0, asynced2 → synced(files0, icache, pcache0), ∀ key. key ∈ pcache0 → key.data?, key.part * VFS_PAGE_SIZE < min(m5, m2) ∨ m0 ≠ key.ino ⊦ m2 ≤ m5 ∧ m2 % VFS_PAGE_SIZE ≠ 0, # truncate(m0, min(m5, m2), pcache0)[key].page = VFS_PAGE_SIZE ∧ key.ino ∈ files0 ∧ ( ¬ truncate(m0, min(m5, m2), pcache0)[key].dirty → key.part ∈ (key.ino = m0 ⊃ mkfile(m5, md0, # links(key.ino, dirs), content0 upto min(m5, m2));files0[key.ino]).content ∧ truncate(m0, min(m5, m2), pcache0)[key].page = (key.ino = m0 ⊃ mkfile(m5, md0, # links(key.ino, dirs), content0 upto min(m5, m2));files0[key.ino]).content[key.part])

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 359:
# buf0 = VFS_PAGE_SIZE, files0[m0] = mkfile(m1, md1, # links(m0, dirs), content0), pcache0[datakey(m0, m2 / VFS_PAGE_SIZE)] = mkpentry(boolvar, buf0), key = datakey(m, m3), key.data?, afs-cons(dirs, files0[m0, mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2))]), afs-cons(dirs, files0), pcache-cons(pcache0, dirs, files0), synced(dirs, icache, pcache0), key ∈ pcache0, m0 ∈ files0, datakey(m0, m2 / VFS_PAGE_SIZE) ∈ pcache0, asynced2 → synced(files0, icache, pcache0), ∀ key. key ∈ pcache0 → key.data?, m3 * VFS_PAGE_SIZE < min(m5, m2) ∨ m0 ≠ m ⊦ # truncate(m0, min(m5, m2), pcache0)[key].page = VFS_PAGE_SIZE ∧ m ∈ files0 ∧ ( ¬ truncate(m0, min(m5, m2), pcache0)[key].dirty → m3 ∈ (m = m0 ⊃ mkfile(m5, md0, # links(m, dirs), content0 upto min(m5, m2));files0[m]).content ∧ truncate(m0, min(m5, m2), pcache0)[key].page = (m = m0 ⊃ mkfile(m5, md0, # links(m, dirs), content0 upto min(m5, m2));files0[m]).content[m3]), m2 ≤ m5 ∧ m2 % VFS_PAGE_SIZE ≠ 0

Rule argument

spec: key name: elim-02 seq: ⊦ key.data? → (m = key.ino ∧ m0 = key.part ↔ key = datakey(m, m0)) subst: [key, m, m0] → [key, m, m3]

Additional information

Used simplifier rules: ⊦ key.data? → (m = key.ino ∧ m0 = key.part ↔ key = datakey(m, m0)); (elim) Used terms: key, m, m3