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Proof step 105 from proof inv-truncate-buff-some (previous step)

# buf-opt.buf = 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(boolvar1, inode0), icache[ino] = mkientry(boolvar0, inode), files0[m3] = mkfile(m1, md1, # links(m3, dirs), content0), truncate(m3, m2, pcache0)[datakey(ino, n)] = mkpentry(boolvar, buf), buf-opt.some?, afs-cons(dirs, files0), afs-cons (dirs, files0[m3, mkfile(m, md, # links(m3, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2)]), synced(files0, icache, pcache0), ino ∈ files0, m3 ∈ files0, m2 ≤ m, ino ∈ icache → ¬ boolvar0, ∀ n. datakey(ino, n) ∈ pcache0 → ¬ pcache0[datakey(ino, n)].dirty, ∀ key. key ∈ pcache0 → key.data? ⊦ 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))] → ¬ boolvar1) ∧ (datakey(ino, n) ∈ pcache0 ∧ (n * VFS_PAGE_SIZE < m2 ∨ m3 ≠ ino) → ¬ boolvar)

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 106:
⊦ key.data? ∧ key ∈ pcache ∧ (key.part * VFS_PAGE_SIZE < size ∨ ino ≠ key.ino) → truncate(ino, size, pcache)[key] = pcache[key]
Proof step 107:
# buf-opt.buf = VFS_PAGE_SIZE, VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, truncate(m3, m2, pcache0)[datakey(ino, n)] = mkpentry(boolvar, buf), files0[m3] = mkfile(m1, md1, # links(m3, dirs), content0), icache[ino] = mkientry(boolvar0, inode), icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, dirs), 0, m))][ino] = mkientry(boolvar1, inode0), buf-opt.some?, afs-cons (dirs, files0[m3, mkfile(m, md, # links(m3, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2)]), afs-cons(dirs, files0), synced(files0, icache, pcache0), m3 ∈ files0, ino ∈ files0, m2 ≤ m, ino ∈ icache → ¬ boolvar0, ∀ 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))] → ¬ boolvar1) ∧ (datakey(ino, n) ∈ pcache0 ∧ (n * VFS_PAGE_SIZE < m2 ∨ m3 ≠ ino) → ¬ boolvar), datakey(ino, n).data? ∧ datakey(ino, n) ∈ pcache0 ∧ (datakey(ino, n).part * VFS_PAGE_SIZE < m2 ∨ m3 ≠ datakey(ino, n).ino)
Proof step 109:
# buf-opt.buf = VFS_PAGE_SIZE, VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, pcache0[datakey(ino, n)] = mkpentry(boolvar, buf), files0[m3] = mkfile(m1, md1, # links(m3, dirs), content0), icache[ino] = mkientry(boolvar0, inode), icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, dirs), 0, m))][ino] = mkientry(boolvar1, inode0), datakey(ino, n).data?, buf-opt.some?, afs-cons (dirs, files0[m3, mkfile(m, md, # links(m3, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2)]), afs-cons(dirs, files0), synced(files0, icache, pcache0), m3 ∈ files0, ino ∈ files0, datakey(ino, n) ∈ pcache0, m2 ≤ m, 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 < m2 ∨ m3 ≠ datakey(ino, n).ino ⊦ 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))] → ¬ boolvar1) ∧ (datakey(ino, n) ∈ pcache0 ∧ (n * VFS_PAGE_SIZE < m2 ∨ m3 ≠ 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] → [m3, m2, pcache0, datakey(ino, n)] flags: <all paths>

Additional information

Used terms: m3, m2, pcache0, datakey(ino, n)