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Proof step 219 from proof refine-unlink (previous step)

# links(entries[str], cache_dirs) = m0 + 1, asynced ↔ false, cache_files[entries[str]] = mkfile(m2, md3, m0 + 1, content), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries[str]] = mkfile(m7, md2, m0 + 1, content0), cache_dirs[m] = mkdir(m1 + 1, md4, # links(m, cache_dirs), m4, entries), afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, c_inode = getinode(entries[str], dirs[ino, dirs[ino].meta:= inode.meta], files), dent = negdentry(mkdentry(str, entries[str]).name), dirs = cache_dirs[m, mkdir(m1, md, # links(m, cache_dirs), m4, entries -- str)], err = ESUCCESS, files = cache_files[entries[str], mkfile(m2, md3, m0, content)], ino = inode.ino, inode = mkinode(entries[str], md0, false, # links(entries[str], cache_dirs), 0, m6), p_inode = (m ∈ dirs[ino, dirs[ino].meta:= inode.meta] ⊃ mkinode (m, dirs[ino, dirs[ino].meta:= inode.meta][m].meta, true, dirs[ino, dirs[ino].meta:= inode.meta][m].nlink, dirs[ino, dirs[ino].meta:= inode.meta][m].nsubdirs, dirs[ino, dirs[ino].meta:= inode.meta][m].size) ;mkinode(m, files[m].meta, false, files[m].nlink, 0, files[m].size) ), 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), str ∈ entries, m ∈ cache_dirs, entries[str] ∈ cache_files, ino ∈ dirs, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ [icache_set#(c_inode, asynced; err, cache_icache); icache_set#(p_inode, asynced; err, cache_icache); dcache_delete#(p_inode.ino, dent.name; err, cache_dcache)] ( icache-cons(cache_icache, dirs[ino, dirs[ino].meta:= inode.meta], files) ∧ dcache-cons(cache_dcache, dirs[ino, dirs[ino].meta:= inode.meta], files) ∧ pcache-cons(cache_pcache, dirs[ino, dirs[ino].meta:= inode.meta], files) ∧ synced(dirs[ino, dirs[ino].meta:= inode.meta], cache_icache, cache_pcache) ∧ (cache_sync → synced(files, cache_icache, cache_pcache)) ∧ afs-cons(dirs[ino, dirs[ino].meta:= inode.meta], files) → ⟨dent0 := mkdentry(str, entries[str]); p_inode0 := mkinode(m, md, true, # links(m, cache_dirs), m4, m1 + 1); p_inode1 := mkinode(entries[str], md0, false, # links(entries[str], cache_dirs), 0, m6); afs_unlink#(; p_inode0, p_inode1, dent0, err0, cache_dirs, afs_files; afs_asynced)⟩ ( cache_dirs = dirs[ino, dirs[ino].meta:= inode.meta] ∧ afs_files = (files ⊕ cache_pcache) ⊕ cache_icache ∧ (afs_asynced ↔ asynced0) ∧ p_inode = p_inode0 ∧ c_inode = p_inode1 ∧ dent = dent0 ∧ err = err0)), ino ∈ files

Heuristic simplifier applied rule simplifier

And closed the goal!

Rule argument

Additional information

Used simplifier rules: ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs → ¬ ino ∈ files; (s)% ⊦ ino ∈ dirs[ino0, ad] ↔ ino ∈ dirs; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)