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Proof step 322 from proof inv-truncate-buff-none-uncached (previous step)

icache[ino] = mkientry(boolvar0, inode), files0[m0] = mkfile(m1, md1, # links(m0, dirs), content0), truncate(m0, min(m5, m2), pcache0)[datakey(ino, n)] = mkpentry(boolvar, buf), icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))][ino] = mkientry(boolvar1, inode0), afs-cons(dirs, files0[m0, mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2))]), afs-cons(dirs, files0), synced(dirs, icache, pcache0), m0 ∈ files0, ino ∈ dirs, ino ∈ icache → ¬ boolvar0, asynced2 → synced(files0, icache, pcache0), ∀ n. datakey(ino, n) ∈ pcache0 → ¬ pcache0[datakey(ino, n)].dirty, ∀ key. key ∈ pcache0 → key.data? ⊦ datakey(m0, m2 / VFS_PAGE_SIZE) ∈ pcache0, (ino ∈ icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))] → ¬ boolvar1) ∧ (datakey(ino, n) ∈ pcache0 ∧ (n * VFS_PAGE_SIZE < min(m5, m2) ∨ m0 ≠ ino) → ¬ boolvar), m2 ≤ m5 ∧ m2 % VFS_PAGE_SIZE ≠ 0 ∧ m2 / VFS_PAGE_SIZE ∈ content0

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 323:
⊦ key.data? ∧ key ∈ pcache ∧ (key.part * VFS_PAGE_SIZE < size ∨ ino ≠ key.ino) → truncate(ino, size, pcache)[key] = pcache[key]
Proof step 324:
icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))][ino] = mkientry(boolvar1, inode0), truncate(m0, min(m5, m2), pcache0)[datakey(ino, n)] = mkpentry(boolvar, buf), files0[m0] = mkfile(m1, md1, # links(m0, dirs), content0), icache[ino] = mkientry(boolvar0, inode), afs-cons(dirs, files0), afs-cons(dirs, files0[m0, mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2))]), synced(dirs, icache, pcache0), ino ∈ dirs, m0 ∈ files0, asynced2 → synced(files0, icache, pcache0), ino ∈ icache → ¬ boolvar0, ∀ key. key ∈ pcache0 → key.data?, ∀ n. datakey(ino, n) ∈ pcache0 → ¬ pcache0[datakey(ino, n)].dirty ⊦ datakey(m0, m2 / VFS_PAGE_SIZE) ∈ pcache0, m2 ≤ m5 ∧ m2 % VFS_PAGE_SIZE ≠ 0 ∧ m2 / VFS_PAGE_SIZE ∈ content0, (ino ∈ icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))] → ¬ boolvar1) ∧ (datakey(ino, n) ∈ pcache0 ∧ (n * VFS_PAGE_SIZE < min(m5, m2) ∨ m0 ≠ ino) → ¬ boolvar), datakey(ino, n).data? ∧ datakey(ino, n) ∈ pcache0 ∧ (datakey(ino, n).part * VFS_PAGE_SIZE < min(m5, m2) ∨ m0 ≠ datakey(ino, n).ino)
Proof step 329:
icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))][ino] = mkientry(boolvar1, inode0), pcache0[datakey(ino, n)] = mkpentry(boolvar, buf), files0[m0] = mkfile(m1, md1, # links(m0, dirs), content0), icache[ino] = mkientry(boolvar0, inode), datakey(ino, n).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), ino ∈ dirs, m0 ∈ files0, datakey(ino, n) ∈ pcache0, asynced2 → synced(files0, icache, pcache0), ino ∈ icache → ¬ boolvar0, ∀ key. key ∈ pcache0 → key.data?, ∀ n. datakey(ino, n) ∈ pcache0 → ¬ pcache0[datakey(ino, n)].dirty, datakey(ino, n).part * VFS_PAGE_SIZE < min(m5, m2) ∨ m0 ≠ datakey(ino, n).ino ⊦ datakey(m0, m2 / VFS_PAGE_SIZE) ∈ pcache0, m2 ≤ m5 ∧ m2 % VFS_PAGE_SIZE ≠ 0 ∧ m2 / VFS_PAGE_SIZE ∈ content0, (ino ∈ icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))] → ¬ boolvar1) ∧ (datakey(ino, n) ∈ pcache0 ∧ (n * VFS_PAGE_SIZE < min(m5, m2) ∨ m0 ≠ ino) → ¬ boolvar)

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(ino, n)] flags: <all paths>

Additional information

Used terms: m0, min(m5, m2), pcache0, datakey(ino, n)