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Proof step 97 from proof inv-truncate-buff-some (previous step)

# buf-opt.buf = VFS_PAGE_SIZE, VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, files0[m3] = mkfile(m1, md1, # links(m3, dirs), content0), 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, m2 ≤ m, ∀ key. key ∈ pcache0 → key.data? ⊦ m2 % VFS_PAGE_SIZE = 0, synced (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)], icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, dirs), 0, m))], truncate(m3, m2, pcache0)[datakey(m3, m2 / VFS_PAGE_SIZE), mkpentry(false, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0))])

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 98:
⊦ synced(files, icache, pcache) → (¬ synced(files0, icache0, pcache0) ↔ ¬(∀ ino. (ino ∈ files → synced(ino, icache, pcache)) → ino ∈ files0 → synced(ino, icache0, pcache0)))
Proof step 99:
# buf-opt.buf = VFS_PAGE_SIZE, VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, 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)]), synced(files0, icache, pcache0), m3 ∈ files0, m2 ≤ m, ∀ key. key ∈ pcache0 → key.data? ⊦ m2 % VFS_PAGE_SIZE = 0, ∀ ino. (ino ∈ files0 → synced(ino, icache, pcache0)) → ino ∈ 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 (ino, icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, dirs), 0, m))], truncate(m3, m2, pcache0)[datakey(m3, m2 / VFS_PAGE_SIZE), mkpentry(false, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0))])

Rule argument

spec: cache-base name: synced-files-variant1 seq: ⊦ synced(files, icache, pcache) → ( ¬ synced(files0, icache0, pcache0) ↔ ¬ (∀ ino. (ino ∈ files → synced(ino, icache, pcache)) → ino ∈ files0 → synced(ino, icache0, pcache0))) subst: [files, icache, pcache, files0, icache0, pcache0] → [files0, icache, pcache0, 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) ], icache [m3, mkientry (false, mkinode(m3, md, false, # links(m3, dirs), 0, m)) ], truncate(m3, m2, pcache0) [datakey(m3, m2 / VFS_PAGE_SIZE), mkpentry (false, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0)) ]] flags: <all paths>

Additional information

Used terms: files0, icache, pcache0, 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) ], icache [m3, mkientry(false, mkinode(m3, md, false, # links(m3, dirs), 0, m)) ], truncate(m3, m2, pcache0) [datakey(m3, m2 / VFS_PAGE_SIZE), mkpentry(false, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0)) ]