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Proof step 168 from proof inv-truncate-buff-none-cached (previous step)

# buf0 = VFS_PAGE_SIZE, VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, icache[ino] = mkientry(boolvar1, inode), truncate(m3, m2, pcache0)[datakey(ino, n)] = mkpentry(true, buf), pcache0[datakey(m3, m2 / VFS_PAGE_SIZE)] = mkpentry(boolvar, buf0), files0[m3] = mkfile(m1, md1, # links(m3, dirs), content0), afs-cons(dirs, files0[m3, mkfile(m, md, # links(m3, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf0, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2)]), afs-cons(dirs, files0), synced(dirs, icache, pcache0), datakey(ino, n) ∈ pcache0, ino ∈ dirs, datakey(m3, m2 / VFS_PAGE_SIZE) ∈ pcache0, m3 ∈ files0, m2 ≤ m, asynced2 → synced(files0, icache, pcache0), ino ∈ icache → ¬ boolvar1, ∀ key. key ∈ pcache0 → key.data?, ∀ n. datakey(ino, n) ∈ pcache0 → ¬ pcache0[datakey(ino, n)].dirty ⊦ m2 % VFS_PAGE_SIZE = 0, datakey(ino, n) = datakey(m3, m2 / VFS_PAGE_SIZE), ino = m3

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 169:
⊦ key.data? ∧ key ∈ pcache ∧ (key.part * VFS_PAGE_SIZE < size ∨ ino ≠ key.ino) → truncate(ino, size, pcache)[key] = pcache[key]
Proof step 170:
# buf0 = VFS_PAGE_SIZE, VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, files0[m3] = mkfile(m1, md1, # links(m3, dirs), content0), pcache0[datakey(m3, m2 / VFS_PAGE_SIZE)] = mkpentry(boolvar, buf0), pcache0[datakey(ino, n)] = mkpentry(true, buf), icache[ino] = mkientry(boolvar1, inode), datakey(ino, n).data?, afs-cons(dirs, files0), afs-cons(dirs, files0[m3, mkfile(m, md, # links(m3, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf0, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2)]), synced(dirs, icache, pcache0), m3 ∈ files0, datakey(m3, m2 / VFS_PAGE_SIZE) ∈ pcache0, ino ∈ dirs, datakey(ino, n) ∈ pcache0, m2 ≤ m, ino ∈ icache → ¬ boolvar1, asynced2 → synced(files0, icache, pcache0), ∀ n. datakey(ino, n) ∈ pcache0 → ¬ pcache0[datakey(ino, n)].dirty, ∀ key. key ∈ pcache0 → key.data?, datakey(ino, n).part * VFS_PAGE_SIZE < m2 ∨ m3 ≠ datakey(ino, n).ino ⊦ m2 % VFS_PAGE_SIZE = 0, datakey(ino, n) = datakey(m3, m2 / VFS_PAGE_SIZE), ino = 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] → [m3, m2, pcache0, datakey(ino, n)] 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: m3, m2, pcache0, datakey(ino, n)