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Proof step 344 from proof inv-truncate-buff-none-cached (previous step)

# buf0 = VFS_PAGE_SIZE, icache[ino] = mkientry(false, inode), 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(ino, n)] = mkpentry(boolvar0, buf), icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))][ino] = mkientry(true, 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), ino ∈ icache, m0 ∈ files0, datakey(m0, m2 / VFS_PAGE_SIZE) ∈ pcache0, ino ∈ dirs, ino ∈ icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))], asynced2 → synced(files0, icache, pcache0), ∀ n. datakey(ino, n) ∈ pcache0 → ¬ pcache0[datakey(ino, n)].dirty, ∀ key. key ∈ pcache0 → key.data? ⊦ m2 ≤ m5 ∧ m2 % VFS_PAGE_SIZE ≠ 0, datakey(ino, n) ∈ pcache0 ∧ (n * VFS_PAGE_SIZE < min(m5, m2) ∨ m0 ≠ ino)

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 345:
⊦ ino ∈ icache[ino0, ie] ↔ ino = ino0 ∨ ino ∈ icache
Proof step 346:
# buf0 = VFS_PAGE_SIZE, icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))][ino] = mkientry(true, inode0), truncate(m0, min(m5, m2), pcache0)[datakey(ino, n)] = mkpentry(boolvar0, buf), pcache0[datakey(m0, m2 / VFS_PAGE_SIZE)] = mkpentry(boolvar, buf0), files0[m0] = mkfile(m1, md1, # links(m0, dirs), content0), icache[ino] = mkientry(false, 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, datakey(m0, m2 / VFS_PAGE_SIZE) ∈ pcache0, m0 ∈ files0, ino ∈ icache, asynced2 → synced(files0, icache, pcache0), ∀ key. key ∈ pcache0 → key.data?, ∀ n. datakey(ino, n) ∈ pcache0 → ¬ pcache0[datakey(ino, n)].dirty, ino = m0 ∨ ino ∈ icache ⊦ datakey(ino, n) ∈ pcache0 ∧ (n * VFS_PAGE_SIZE < min(m5, m2) ∨ m0 ≠ ino), m2 ≤ m5 ∧ m2 % VFS_PAGE_SIZE ≠ 0

Rule argument

spec: store, inst: icache name: In-insert seq: ⊦ ino ∈ icache[ino0, ie] ↔ ino = ino0 ∨ ino ∈ icache subst: [ino, icache, ino0, ie] → [ino, icache, m0, mkientry (false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))] flags: <all paths>

Additional information

Used terms: ino, icache, m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))