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Proof step 46 from proof inv-writepage (previous step)

# buf = VFS_PAGE_SIZE, files[m] = mkfile(m0, md, # links(m, dirs), content), afs-cons(dirs, files), afs-cons(dirs, files[m, mkfile(m0, md, # links(m, dirs), content[pageno, buf])]), synced(files, icache, pcache), m ∈ files ⊦ synced(files[m, mkfile(m0, md, # links(m, dirs), content[pageno, buf])], icache, pcache[datakey(m, pageno), mkpentry(false, buf)])

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 47:
⊦ synced(files, icache, pcache) → (¬ synced(files0, icache0, pcache0) ↔ ¬(∀ ino. (ino ∈ files → synced(ino, icache, pcache)) → ino ∈ files0 → synced(ino, icache0, pcache0)))
Proof step 48:
# buf = VFS_PAGE_SIZE, files[m] = mkfile(m0, md, # links(m, dirs), content), afs-cons(dirs, files[m, mkfile(m0, md, # links(m, dirs), content[pageno, buf])]), afs-cons(dirs, files), synced(files, icache, pcache), m ∈ files ⊦ ∀ ino. (ino ∈ files → synced(ino, icache, pcache)) → ino ∈ files[m, mkfile(m0, md, # links(m, dirs), content[pageno, buf])] → synced(ino, icache, pcache[datakey(m, pageno), mkpentry(false, buf)])

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] → [files, icache, pcache, files [m, mkfile(m0, md, # links(m, dirs), content[pageno, buf]) ], icache, pcache[datakey(m, pageno), mkpentry(false, buf)]] flags: <all paths>

Additional information

Used terms: files, icache, pcache, files[m, mkfile(m0, md, # links(m, dirs), content[pageno, buf])], icache, pcache[datakey(m, pageno), mkpentry(false, buf)]