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Proof step 16 from proof refine-unlink (previous step)

cache_files[entries[str]] = mkfile(m2, md0, # links(entries[str], cache_dirs), content0), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries[str]] = mkfile(m0, md, m1, content), cache_dirs[m] = mkdir(m3, md1, # links(m, cache_dirs), m5, entries), afs-cons(cache_dirs, cache_files), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), dcache-cons(cache_dcache, cache_dirs, cache_files), icache-cons(cache_icache, cache_dirs, cache_files), pcache-cons(cache_pcache, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache), m ∈ cache_dirs, str ∈ entries, entries[str] ∈ cache_files, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ m1 = # links(entries[str], cache_dirs)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 17:
⊦ icache-cons(icache, dirs, files) ↔ (∀ ino. ino ∈ icache → icache[ino].inode.ino = ino ∧ (icache[ino].dirty ⊃ valid-file-inode(icache[ino].inode, dirs, files) ;valid-ino(ino, dirs, files) ∧ valid-inode(icache[ino].inode, dirs, files) ))
Proof step 18:
cache_dirs[m] = mkdir(m3, md1, # links(m, cache_dirs), m5, entries), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries[str]] = mkfile(m0, md, m1, content), cache_files[entries[str]] = mkfile(m2, md0, # links(entries[str], cache_dirs), content0), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), afs-cons(cache_dirs, cache_files), dcache-cons(cache_dcache, cache_dirs, cache_files), pcache-cons(cache_pcache, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache), entries[str] ∈ cache_files, str ∈ entries, m ∈ cache_dirs, cache_sync → synced(cache_files, cache_icache, cache_pcache), ∀ ino. ino ∈ cache_icache → cache_icache[ino].inode.ino = ino ∧ (cache_icache[ino].dirty ⊃ valid-file-inode(cache_icache[ino].inode, cache_dirs, cache_files) ;valid-ino(ino, cache_dirs, cache_files) ∧ valid-inode(cache_icache[ino].inode, cache_dirs, cache_files) ), links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ m1 = # links(entries[str], cache_dirs)

Rule argument

spec: cache-base name: icache-cons seq: ⊦ icache-cons(icache, dirs, files) ↔ (∀ ino. ino ∈ icache → icache[ino].inode.ino = ino ∧ (icache[ino].dirty ⊃ valid-file-inode(icache[ino].inode, dirs, files) ; valid-ino(ino, dirs, files) ∧ valid-inode(icache[ino].inode, dirs, files) )) subst: [files, dirs, icache] → [cache_files, cache_dirs, cache_icache] flags: <all paths>

Additional information

Used terms: cache_files, cache_dirs, cache_icache