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Proof step 172 from proof inv-writepage (previous step)

# buf = VFS_PAGE_SIZE, afs-cons(dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), m ∈ files ⊦ ∀ key. key ∈ pcache[datakey(m, pageno), mkpentry(true, buf)] → key.data? ∧ # pcache[datakey(m, pageno), mkpentry(true, buf)][key].page = VFS_PAGE_SIZE ∧ valid-file-ino(key.ino, dirs, files) ∧ ( ¬ pcache[datakey(m, pageno), mkpentry(true, buf)][key].dirty → key.part ∈ files[key.ino].content ∧ pcache[datakey(m, pageno), mkpentry(true, buf)][key].page = files[key.ino].content[key.part])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 173:
# buf = VFS_PAGE_SIZE, afs-cons(dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), key ∈ pcache[datakey(m, pageno), mkpentry(true, buf)], m ∈ files ⊦ key.data? ∧ # pcache[datakey(m, pageno), mkpentry(true, buf)][key].page = VFS_PAGE_SIZE ∧ key.ino ∈ files ∧ ( ¬ pcache[datakey(m, pageno), mkpentry(true, buf)][key].dirty → key.part ∈ files[key.ino].content ∧ pcache[datakey(m, pageno), mkpentry(true, buf)][key].page = files[key.ino].content[key.part])

Rule argument

Additional information

Used simplifier rules: ⊦ valid-file-ino(ino, dirs, files) ↔ ino ∈ files; (s)