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Proof step 300 from proof refine-rmdir (previous step)

cache_dirs[m] = mkdir(m0 + 1, md2, # links(m, cache_dirs), m1 + 1, entries), cache_dirs[entries[str]] = mkdir(m2, md1, # links(entries[str], cache_dirs), m4, ∅), afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, dirs = cache_dirs[m, mkdir(m0, md2, # links(m, cache_dirs), m1, entries -- str)], files = afs_files, ino = mkdentry(str, entries[str]).ino, mkdentry(str, entries[str]).dentry?, 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), entries[str] ∈ cache_dirs, m ∈ cache_dirs, str ∈ entries, ⌊err0⌋ , cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟨if ino ∈ dirs then dirs[ino].nlink := dirs[ino].nlink - 1; if ino ∈ files then files[ino].nlink := files[ino].nlink - 1; dent := negdentry(mkdentry(str, entries[str]).name); afs_inode_sync#(mkinode(m, md, true, # links(m, cache_dirs), m1 + 1, m0 + 1); dirs, files); afs_inode_sync#(mkinode(entries[str], md0, true, # links(entries[str], cache_dirs), m4, m2); dirs, files); p_inode := (m ∈ dirs ⊃ mkinode(m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode(m, files[m].meta, false, files[m].nlink, 0, files[m].size) ); c_inode := getinode(entries[str], dirs, files); err := ESUCCESS; asynced := ?⟩ ( dirs = cache_dirs ∧ files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ (asynced ↔ asynced0) ∧ mkinode(m, md, true, # links(m, cache_dirs), m1 + 1, m0 + 1) = p_inode ∧ mkinode(entries[str], md0, true, # links(entries[str], cache_dirs), m4, m2) = c_inode ∧ mkdentry(str, entries[str]) = dent ∧ err0 = err), ⟨fail#(; ; err); asynced := ?⟩ ((asynced ↔ asynced0) ∧ err0 = err), entries[str] = ROOT_INO

Heuristic symbolic execution applied rule if positive right

And obtained the following new goals

Proof step 301:
cache_dirs[entries[str]] = mkdir(m2, md1, # links(entries[str], cache_dirs), m4, ∅), cache_dirs[m] = mkdir(m0 + 1, md2, # links(m, cache_dirs), m1 + 1, entries), afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, dirs = cache_dirs[m, mkdir(m0, md2, # links(m, cache_dirs), m1, entries -- str)], files = afs_files, ino = mkdentry(str, entries[str]).ino, mkdentry(str, entries[str]).dentry?, 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), str ∈ entries, m ∈ cache_dirs, entries[str] ∈ cache_dirs, ⌊err0⌋ , cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟨dirs[ino].nlink := dirs[ino].nlink - 1; if ino ∈ files then files[ino].nlink := files[ino].nlink - 1; dent := negdentry(mkdentry(str, entries[str]).name); afs_inode_sync#(mkinode(m, md, true, # links(m, cache_dirs), m1 + 1, m0 + 1); dirs, files); afs_inode_sync#(mkinode(entries[str], md0, true, # links(entries[str], cache_dirs), m4, m2); dirs, files); p_inode := (m ∈ dirs ⊃ mkinode(m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode(m, files[m].meta, false, files[m].nlink, 0, files[m].size) ); c_inode := getinode(entries[str], dirs, files); err := ESUCCESS; asynced := ?⟩ ( dirs = cache_dirs ∧ files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ (asynced ↔ asynced0) ∧ mkinode(m, md, true, # links(m, cache_dirs), m1 + 1, m0 + 1) = p_inode ∧ mkinode(entries[str], md0, true, # links(entries[str], cache_dirs), m4, m2) = c_inode ∧ mkdentry(str, entries[str]) = dent ∧ err0 = err), ⟨fail#(; ; err); asynced := ?⟩ ((asynced ↔ asynced0) ∧ err0 = err), entries[str] = ROOT_INO

Rule argument

pos: right 1

Additional information

Used simplifier rules: ⊦ mkdentry(str, m).ino = m; (s)% ⊦ ino ∈ dirs[ino0, ad] ↔ ino ∈ dirs; (s)