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Proof step 199 from proof inv-truncate-buff-none-cached (previous step)

# buf1 = VFS_PAGE_SIZE, # buf0 = VFS_PAGE_SIZE, (m6 = m3 ⊃ mkfile(m, md, # links(m3, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf0, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ;mkfile(m5, md2, # links(m6, dirs), content1) ) = mkfile(m0, md0, m4, content), VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, truncate(m3, m2, pcache0)[datakey(m6, m7)] = mkpentry(boolvar0, buf), files0[m6] = mkfile(m5, md2, # links(m6, dirs), content1), pcache0[datakey(m6, m7)] = mkpentry(boolvar1, buf1), files0[m3] = mkfile(m1, md1, # links(m3, dirs), content0), pcache0[datakey(m3, m2 / VFS_PAGE_SIZE)] = mkpentry(boolvar, buf0), 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), m6 ∈ files0, datakey(m6, m7) ∈ pcache0, m3 ∈ files0, datakey(m3, m2 / VFS_PAGE_SIZE) ∈ pcache0, m2 ≤ m, ¬ boolvar1 → m7 ∈ content1 ∧ buf1 = content1[m7], asynced2 → synced(files0, icache, pcache0), ∀ key0. key0 ∈ pcache0 → key0.data? ∧ # pcache0[key0].page = VFS_PAGE_SIZE ∧ key0.ino ∈ files0 ∧ (¬ pcache0[key0].dirty → key0.part ∈ files0[key0.ino].content ∧ pcache0[key0].page = files0[key0.ino].content[key0.part]), ∀ key. key ∈ pcache0 → key.data?, m7 * VFS_PAGE_SIZE < m2 ∨ m3 ≠ m6 ⊦ m2 % VFS_PAGE_SIZE = 0, datakey(m6, m7) = datakey(m3, m2 / VFS_PAGE_SIZE), # buf = VFS_PAGE_SIZE ∧ (¬ boolvar0 → m7 ∈ content ∧ buf = content[m7])

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 200:
⊦ key.data? ∧ key ∈ pcache ∧ (key.part * VFS_PAGE_SIZE < size ∨ ino ≠ key.ino) → truncate(ino, size, pcache)[key] = pcache[key]
Proof step 201:
# buf0 = VFS_PAGE_SIZE, # buf1 = VFS_PAGE_SIZE, (m6 = m3 ⊃ mkfile(m, md, # links(m3, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf0, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ;mkfile(m5, md2, # links(m6, dirs), content1) ) = mkfile(m0, md0, m4, content), VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, pcache0[datakey(m3, m2 / VFS_PAGE_SIZE)] = mkpentry(boolvar, buf0), files0[m3] = mkfile(m1, md1, # links(m3, dirs), content0), pcache0[datakey(m6, m7)] = mkpentry(boolvar1, buf1), files0[m6] = mkfile(m5, md2, # links(m6, dirs), content1), pcache0[datakey(m6, m7)] = mkpentry(boolvar0, buf), datakey(m6, m7).data?, 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), datakey(m3, m2 / VFS_PAGE_SIZE) ∈ pcache0, m3 ∈ files0, m6 ∈ files0, datakey(m6, m7) ∈ pcache0, m2 ≤ m, asynced2 → synced(files0, icache, pcache0), ¬ boolvar1 → m7 ∈ content1 ∧ buf1 = content1[m7], ∀ key. key ∈ pcache0 → key.data?, ∀ key0. key0 ∈ pcache0 → key0.data? ∧ # pcache0[key0].page = VFS_PAGE_SIZE ∧ key0.ino ∈ files0 ∧ (¬ pcache0[key0].dirty → key0.part ∈ files0[key0.ino].content ∧ pcache0[key0].page = files0[key0.ino].content[key0.part]), m7 * VFS_PAGE_SIZE < m2 ∨ m3 ≠ m6, datakey(m6, m7).part * VFS_PAGE_SIZE < m2 ∨ m3 ≠ datakey(m6, m7).ino ⊦ m2 % VFS_PAGE_SIZE = 0, datakey(m6, m7) = datakey(m3, m2 / VFS_PAGE_SIZE), # buf = VFS_PAGE_SIZE ∧ (¬ boolvar0 → m7 ∈ content ∧ buf = content[m7])

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(m6, m7)] flags: <all paths>

Additional information

Used simplifier rules: ⊦ datakey(m, m0).data?; (s)% ⊦ datakey(m, m0).part = m0; (s)% ⊦ datakey(m, m0).ino = m; (s) Used terms: m3, m2, pcache0, datakey(m6, m7)