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Proof step 173 from proof inv-write_inode (previous step)

dirs[m] = mkdir(m0, md0, # links(m, dirs), m2, entries), afs-cons(dirs[m, mkdir(m0, md, # links(m, dirs), m2, entries)], files), afs-cons(dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), m ∈ dirs, asynced2 → synced(files, icache, pcache) ⊦ m ∈ icache, ∀ key. key ∈ pcache → key.data? ∧ # pcache[key].page = VFS_PAGE_SIZE ∧ valid-file-ino(key.ino, dirs[m, mkdir(m0, md, # links(m, dirs), m2, entries)], files) ∧ (¬ pcache[key].dirty → key.part ∈ files[key.ino].content ∧ pcache[key].page = files[key.ino].content[key.part])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 174:
dirs[m] = mkdir(m0, md0, # links(m, dirs), m2, entries), afs-cons(dirs, files), afs-cons(dirs[m, mkdir(m0, md, # links(m, dirs), m2, entries)], files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), key ∈ pcache, m ∈ dirs, asynced2 → synced(files, icache, pcache) ⊦ m ∈ icache, key.data? ∧ # pcache[key].page = VFS_PAGE_SIZE ∧ key.ino ∈ files ∧ (¬ pcache[key].dirty → key.part ∈ files[key.ino].content ∧ pcache[key].page = files[key.ino].content[key.part])

Rule argument

Additional information

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