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Proof step 158 from proof inv-truncate-buff-none-uncached (previous step)

VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, files1[m3] = mkfile(m1, md1, # links(m3, dirs), content0), afs-cons (dirs, files1 [m3, mkfile(m, md, # links(m3, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ]), afs-cons(dirs, files1), pcache-cons(pcache0, dirs, files1), synced(dirs, icache, pcache0), m3 ∈ files1, m2 / VFS_PAGE_SIZE ∈ content0, m2 ≤ m, asynced2 → synced(files1, icache, pcache0), ∀ key. key ∈ pcache0 → key.data? ⊦ m2 % VFS_PAGE_SIZE = 0, pcache-cons (truncate(m3, m2, pcache0)[datakey(m3, m2 / VFS_PAGE_SIZE), mkpentry(false, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0))], dirs, files1 [m3, mkfile(m, md, # links(m3, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ]), datakey(m3, m2 / VFS_PAGE_SIZE) ∈ pcache0

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 159:
⊦ pcache-cons(pcache, dirs, files) ↔ (∀ key. key ∈ pcache → key.data? ∧ # pcache[key].page = VFS_PAGE_SIZE ∧ valid-file-ino(key.ino, dirs, files) ∧ (¬ pcache[key].dirty → key.part ∈ files[key.ino].content ∧ pcache[key].page = files[key.ino].content[key.part]))
Proof step 160:
VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, files1[m3] = mkfile(m1, md1, # links(m3, dirs), content0), afs-cons(dirs, files1), afs-cons (dirs, files1 [m3, mkfile(m, md, # links(m3, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ]), pcache-cons(pcache0, dirs, files1), synced(dirs, icache, pcache0), m2 / VFS_PAGE_SIZE ∈ content0, m3 ∈ files1, m2 ≤ m, asynced2 → synced(files1, icache, pcache0), ∀ key. key ∈ pcache0 → key.data? ⊦ m2 % VFS_PAGE_SIZE = 0, datakey(m3, m2 / VFS_PAGE_SIZE) ∈ pcache0, ∀ key. key ∈ truncate(m3, m2, pcache0)[datakey(m3, m2 / VFS_PAGE_SIZE), mkpentry(false, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0))] → key.data? ∧ # truncate(m3, m2, pcache0) [datakey(m3, m2 / VFS_PAGE_SIZE), mkpentry(false, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)) ] [key ] .page = VFS_PAGE_SIZE ∧ valid-file-ino (key.ino, dirs, files1 [m3, mkfile(m, md, # links(m3, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ]) ∧ ( ¬ truncate(m3, m2, pcache0) [datakey(m3, m2 / VFS_PAGE_SIZE), mkpentry(false, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)) ] [key ] .dirty → key.part ∈ files1 [m3, mkfile (m, md, # links(m3, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ] [key.ino ] .content ∧ truncate(m3, m2, pcache0) [datakey(m3, m2 / VFS_PAGE_SIZE), mkpentry(false, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)) ] [key ] .page = files1 [m3, mkfile (m, md, # links(m3, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ] [key.ino ] .content [key.part ])

Rule argument

spec: cache-base name: pcache-cons seq: ⊦ pcache-cons(pcache, dirs, files) ↔ (∀ key. key ∈ pcache → key.data? ∧ # pcache[key].page = VFS_PAGE_SIZE ∧ valid-file-ino(key.ino, dirs, files) ∧ ( ¬ pcache[key].dirty → key.part ∈ files[key.ino].content ∧ pcache[key].page = files[key.ino].content[key.part])) subst: [pcache, dirs, files] → [truncate(m3, m2, pcache0) [datakey(m3, m2 / VFS_PAGE_SIZE), mkpentry (false, fill (content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)) ], dirs, files1 [m3, mkfile (m, md, # links(m3, dirs), content0 [m2 / VFS_PAGE_SIZE, fill (content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0) ] upto m2) ]] flags: <all paths>

Additional information

Used terms: truncate(m3, m2, pcache0) [datakey(m3, m2 / VFS_PAGE_SIZE), mkpentry (false, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)) ], dirs, files1 [m3, mkfile (m, md, # links(m3, dirs), content0 [m2 / VFS_PAGE_SIZE, fill (content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0) ] upto m2) ]