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Proof step 7 from proof refine-unlink (previous step)

c_inode.ino = cache_dirs[p_inode.ino].entries[str], p_inode.nlink = cache_dirs[p_inode.ino].nlink, c_inode.nlink = ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[c_inode.ino].nlink, p_inode.nsubdirs = cache_dirs[p_inode.ino].nsubdirs, c_inode.nsubdirs = 0, p_inode.size = cache_dirs[p_inode.ino].size, p_inode.directory, afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), afs-cons(cache_dirs, cache_files), 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), c_inode.ino ∈ cache_files, str ∈ cache_dirs[p_inode.ino].entries, p_inode.ino ∈ cache_dirs, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(p_inode.ino, cache_dirs) ≠ ∅ ∨ p_inode.ino = ROOT_INO ⊦ c_inode.nlink = cache_files[c_inode.ino].nlink, c_inode.directory

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 8:
c_inode.ino = cache_dirs[m].entries[str], c_inode.nlink = ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[c_inode.ino].nlink, c_inode.nsubdirs = 0, boolvar, m0 = cache_dirs[m].nlink, m1 = cache_dirs[m].nsubdirs, m2 = cache_dirs[m].size, p_inode = mkinode(m, md, boolvar, m0, m1, m2), 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 ∈ cache_dirs[m].entries, c_inode.ino ∈ cache_files, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ c_inode.nlink = cache_files[c_inode.ino].nlink, c_inode.directory

Rule argument

spec: inode name: elim seq: ⊦ ( ( ( (m = inode.ino ∧ md = inode.meta) ∧ (boolvar ↔ inode.directory)) ∧ m0 = inode.nlink) ∧ m1 = inode.nsubdirs) ∧ m2 = inode.size ↔ inode = mkinode(m, md, boolvar, m0, m1, m2) subst: [inode, m, md, boolvar, m0, m1, m2] → [p_inode, m, md, boolvar, m0, m1, m2]

Additional information

Used simplifier rules: ⊦ ( ( ( (m = inode.ino ∧ md = inode.meta) ∧ (boolvar ↔ inode.directory)) ∧ m0 = inode.nlink) ∧ m1 = inode.nsubdirs) ∧ m2 = inode.size ↔ inode = mkinode(m, md, boolvar, m0, m1, m2); (elim) Used terms: p_inode, m, md, boolvar, m0, m1, m2