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Proof step 164 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), files0[m3] = mkfile(m1, md1, # links(m3, dirs), content0), pcache0[datakey(m3, m2 / VFS_PAGE_SIZE)] = mkpentry(boolvar, buf0), truncate(m3, m2, pcache0)[datakey(m3, m2 / VFS_PAGE_SIZE), mkpentry(false, fill(buf0, zero, m2 % VFS_PAGE_SIZE, n0))][datakey(ino, n)] = mkpentry(boolvar0, buf), icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, dirs), 0, m))][ino] = mkientry(boolvar2, inode0), 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, 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? ⊦ m2 % VFS_PAGE_SIZE = 0, (ino ∈ icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, dirs), 0, m))] → ¬ boolvar2) ∧ ( datakey(ino, n) ∈ truncate(m3, m2, pcache0)[datakey(m3, m2 / VFS_PAGE_SIZE), mkpentry(false, fill(buf0, zero, m2 % VFS_PAGE_SIZE, n0))] → ¬ boolvar0)

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 165:
# buf0 = VFS_PAGE_SIZE, VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, dirs), 0, m))][ino] = mkientry(boolvar2, inode0), truncate(m3, m2, pcache0)[datakey(m3, m2 / VFS_PAGE_SIZE), mkpentry(false, fill(buf0, zero, m2 % VFS_PAGE_SIZE, n0))][datakey(ino, n)] = mkpentry(boolvar0, buf), pcache0[datakey(m3, m2 / VFS_PAGE_SIZE)] = mkpentry(boolvar, buf0), files0[m3] = mkfile(m1, md1, # links(m3, dirs), content0), icache[ino] = mkientry(boolvar1, inode), 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), 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 ∈ icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, dirs), 0, m))] → ¬ boolvar2) ∧ ( datakey(ino, n) ∈ truncate(m3, m2, pcache0)[datakey(m3, m2 / VFS_PAGE_SIZE), mkpentry(false, fill(buf0, zero, m2 % VFS_PAGE_SIZE, n0))] → ¬ boolvar0)

Rule argument

fma: datakey(ino, n) = datakey(m3, m2 / VFS_PAGE_SIZE)

Additional information

Used simplifier rules: ⊦ datakey(m, m0) = datakey(m1, m2) ↔ m = m1 ∧ m0 = m2; (ws)% ⊦ ino = ino0 → icache[ino0, ie][ino] = ie; (s)%⊦ mkientry(boolvar, inode) = mkientry(boolvar0, inode0) ↔ (boolvar ↔ boolvar0) ∧ inode = inode0; (ws)% ⊦ pcache[key, pe][key] = pe; (s)%⊦ mkpentry(boolvar, buf) = mkpentry(boolvar0, buf0) ↔ (boolvar ↔ boolvar0) ∧ buf = buf0; (ws) Used formulas: datakey(ino, n) = datakey(m3, m2 / VFS_PAGE_SIZE)