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Proof step 146 from proof inv-truncate-buff-some (previous step)

# buf-opt.buf = VFS_PAGE_SIZE, (key.ino = m3 ⊃ mkfile(m, md, # links(key.ino, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ;files0[key.ino] ) = mkfile(m0, md0, m4, content), VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, truncate(m3, m2, pcache0)[datakey(m3, m2 / VFS_PAGE_SIZE), mkpentry(false, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0))][key] = mkpentry(boolvar, buf), files0[m3] = mkfile(m1, md1, # links(m3, dirs), content0), 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)]), pcache-cons(pcache0, dirs, files0), synced(dirs, icache, pcache0), key ∈ truncate(m3, m2, pcache0)[datakey(m3, m2 / VFS_PAGE_SIZE), mkpentry(false, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0))], m3 ∈ files0, m2 ≤ m, asynced1 → synced(files0, icache, pcache0), ∀ key. key ∈ pcache0 → key.data? ⊦ m2 % VFS_PAGE_SIZE = 0, key.data? ∧ # buf = VFS_PAGE_SIZE ∧ key.ino ∈ files0 ∧ (¬ boolvar → key.part ∈ content ∧ buf = content[key.part])

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 147:
⊦ 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 148:
# buf-opt.buf = VFS_PAGE_SIZE, (key.ino = m3 ⊃ mkfile(m, md, # links(key.ino, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ;files0[key.ino] ) = mkfile(m0, md0, m4, content), VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, files0[m3] = mkfile(m1, md1, # links(m3, dirs), content0), truncate(m3, m2, pcache0)[datakey(m3, m2 / VFS_PAGE_SIZE), mkpentry(false, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0))][key] = mkpentry(boolvar, buf), 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(dirs, icache, pcache0), m3 ∈ files0, key ∈ truncate(m3, m2, pcache0)[datakey(m3, m2 / VFS_PAGE_SIZE), mkpentry(false, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0))], m2 ≤ m, asynced1 → synced(files0, icache, pcache0), ∀ key. key ∈ pcache0 → key.data?, ∀ key. key ∈ pcache0 → key.data? ∧ # pcache0[key].page = VFS_PAGE_SIZE ∧ valid-file-ino(key.ino, dirs, files0) ∧ (¬ pcache0[key].dirty → key.part ∈ files0[key.ino].content ∧ pcache0[key].page = files0[key.ino].content[key.part]) ⊦ m2 % VFS_PAGE_SIZE = 0, key.data? ∧ # buf = VFS_PAGE_SIZE ∧ key.ino ∈ files0 ∧ (¬ boolvar → key.part ∈ content ∧ buf = 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] → [pcache0, dirs, files0] flags: <all paths>

Additional information

Used terms: pcache0, dirs, files0