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Proof step 281 from proof inv-truncate-buff-some (previous step)

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

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 282:
⊦ key.data? ∧ key ∈ pcache ∧ (key.part * VFS_PAGE_SIZE < size ∨ ino ≠ key.ino) → truncate(ino, size, pcache)[key] = pcache[key]
Proof step 283:
# buf-opt.buf = VFS_PAGE_SIZE, icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))][ino] = mkientry(boolvar1, inode0), truncate(m0, min(m5, m2), pcache)[datakey(ino, n)] = mkpentry(boolvar, buf), files0[m0] = mkfile(m1, md1, # links(m0, dirs), content0), icache[ino] = mkientry(boolvar0, inode), buf-opt.some?, afs-cons(dirs, files0), afs-cons(dirs, files0[m0, mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2))]), synced(files0, icache, pcache), m0 ∈ files0, ino ∈ files0, ino ∈ icache → ¬ boolvar0, ∀ key. key ∈ pcache → key.data?, ∀ n. datakey(ino, n) ∈ pcache → ¬ pcache[datakey(ino, n)].dirty ⊦ m2 ≤ m5 ∧ m2 % VFS_PAGE_SIZE ≠ 0, (ino ∈ icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))] → ¬ boolvar1) ∧ (datakey(ino, n) ∈ pcache ∧ (n * VFS_PAGE_SIZE < min(m5, m2) ∨ m0 ≠ ino) → ¬ boolvar), datakey(ino, n).data? ∧ datakey(ino, n) ∈ pcache ∧ (datakey(ino, n).part * VFS_PAGE_SIZE < min(m5, m2) ∨ m0 ≠ datakey(ino, n).ino)
Proof step 285:
# buf-opt.buf = VFS_PAGE_SIZE, icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))][ino] = mkientry(boolvar1, inode0), pcache[datakey(ino, n)] = mkpentry(boolvar, buf), files0[m0] = mkfile(m1, md1, # links(m0, dirs), content0), icache[ino] = mkientry(boolvar0, inode), datakey(ino, n).data?, buf-opt.some?, afs-cons(dirs, files0), afs-cons(dirs, files0[m0, mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2))]), synced(files0, icache, pcache), m0 ∈ files0, ino ∈ files0, datakey(ino, n) ∈ pcache, ino ∈ icache → ¬ boolvar0, ∀ key. key ∈ pcache → key.data?, ∀ n. datakey(ino, n) ∈ pcache → ¬ pcache[datakey(ino, n)].dirty, datakey(ino, n).part * VFS_PAGE_SIZE < min(m5, m2) ∨ m0 ≠ datakey(ino, n).ino ⊦ m2 ≤ m5 ∧ m2 % VFS_PAGE_SIZE ≠ 0, (ino ∈ icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))] → ¬ boolvar1) ∧ (datakey(ino, n) ∈ pcache ∧ (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), pcache, datakey(ino, n)] flags: <all paths>

Additional information

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