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Proof step 65 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(dirs, icache, pcache), m ∈ files ⊦ ∀ ino. (ino ∈ dirs → synced(ino, icache, pcache)) → ino ∈ dirs → synced(ino, icache, pcache[datakey(m, pageno), mkpentry(false, buf)])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 66:
# buf = VFS_PAGE_SIZE, files[m] = mkfile(m0, md, # links(m, dirs), content), pcache[datakey(m, pageno), mkpentry(false, buf)][datakey(ino, n)].dirty, afs-cons(dirs, files[m, mkfile(m0, md, # links(m, dirs), content[pageno, buf])]), afs-cons(dirs, files), synced(dirs, icache, pcache), ino ∈ dirs, m ∈ files, datakey(ino, n) ∈ pcache[datakey(m, pageno), mkpentry(false, buf)], ino ∈ icache → ¬ icache[ino].dirty, ∀ n. datakey(ino, n) ∈ pcache → ¬ pcache[datakey(ino, n)].dirty ⊦

Rule argument

Additional information

Used simplifier rules: ⊦ synced(ino, icache, pcache) ↔ (ino ∈ icache → ¬ icache[ino].dirty) ∧ (∀ n. datakey(ino, n) ∈ pcache → ¬ pcache[datakey(ino, n)].dirty); (s)