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Proof step 367 from proof inv-truncate-buff-none-cached (previous step)

# buf0 = VFS_PAGE_SIZE, (m = m0 ⊃ mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2));files0[m]) = mkfile(m4, md, m6, content), files0[m0] = mkfile(m1, md1, # links(m0, dirs), content0), pcache0[datakey(m0, m2 / VFS_PAGE_SIZE)] = mkpentry(boolvar, buf0), truncate(m0, min(m5, m2), pcache0)[datakey(m, m3)] = mkpentry(boolvar0, buf), afs-cons(dirs, files0[m0, mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2))]), afs-cons(dirs, files0), synced(dirs, icache, pcache0), datakey(m, m3) ∈ pcache0, m0 ∈ files0, datakey(m0, m2 / VFS_PAGE_SIZE) ∈ pcache0, asynced2 → synced(files0, icache, pcache0), ¬ boolvar → m2 / VFS_PAGE_SIZE ∈ content0 ∧ buf0 = content0[m2 / VFS_PAGE_SIZE], ∀ key. key ∈ pcache0 → key.data? ∧ # pcache0[key].page = VFS_PAGE_SIZE ∧ key.ino ∈ files0 ∧ (¬ pcache0[key].dirty → key.part ∈ files0[key.ino].content ∧ pcache0[key].page = files0[key.ino].content[key.part]), ∀ key. key ∈ pcache0 → key.data?, m3 * VFS_PAGE_SIZE < min(m5, m2) ∨ m0 ≠ m ⊦ # buf = VFS_PAGE_SIZE ∧ m ∈ files0 ∧ (¬ boolvar0 → m3 ∈ content ∧ buf = content[m3]), m2 ≤ m5 ∧ m2 % VFS_PAGE_SIZE ≠ 0

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 368:
⊦ key.data? ∧ key ∈ pcache ∧ (key.part * VFS_PAGE_SIZE < size ∨ ino ≠ key.ino) → truncate(ino, size, pcache)[key] = pcache[key]
Proof step 369:
# buf0 = VFS_PAGE_SIZE, (m = m0 ⊃ mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2));files0[m]) = mkfile(m4, md, m6, content), pcache0[datakey(m, m3)] = mkpentry(boolvar0, buf), pcache0[datakey(m0, m2 / VFS_PAGE_SIZE)] = mkpentry(boolvar, buf0), files0[m0] = mkfile(m1, md1, # links(m0, dirs), content0), datakey(m, m3).data?, afs-cons(dirs, files0), afs-cons(dirs, files0[m0, mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2))]), synced(dirs, icache, pcache0), datakey(m0, m2 / VFS_PAGE_SIZE) ∈ pcache0, m0 ∈ files0, datakey(m, m3) ∈ pcache0, ¬ boolvar → m2 / VFS_PAGE_SIZE ∈ content0 ∧ buf0 = content0[m2 / VFS_PAGE_SIZE], asynced2 → synced(files0, icache, pcache0), ∀ key. key ∈ pcache0 → key.data?, ∀ key. key ∈ pcache0 → key.data? ∧ # pcache0[key].page = VFS_PAGE_SIZE ∧ key.ino ∈ files0 ∧ (¬ pcache0[key].dirty → key.part ∈ files0[key.ino].content ∧ pcache0[key].page = files0[key.ino].content[key.part]), m3 * VFS_PAGE_SIZE < min(m5, m2) ∨ m0 ≠ m, datakey(m, m3).part * VFS_PAGE_SIZE < min(m5, m2) ∨ m0 ≠ datakey(m, m3).ino ⊦ m2 ≤ m5 ∧ m2 % VFS_PAGE_SIZE ≠ 0, # buf = VFS_PAGE_SIZE ∧ m ∈ files0 ∧ (¬ boolvar0 → m3 ∈ content ∧ buf = content[m3])

Rule argument

spec: pcache-del-ops name: at-truncate seq: ⊦ key.data? ∧ key ∈ pcache ∧ (key.part * VFS_PAGE_SIZE < size ∨ ino ≠ key.ino) → truncate(ino, size, pcache)[key] = pcache[key] subst: [ino, size, pcache, key] → [m0, min(m5, m2), pcache0, datakey(m, m3)] flags: <all paths>

Additional information

Used simplifier rules: ⊦ datakey(m, m0).data?; (s)% ⊦ datakey(m, m0).part = m0; (s)% ⊦ datakey(m, m0).ino = m; (s) Used terms: m0, min(m5, m2), pcache0, datakey(m, m3)