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Proof step 279 from proof refine-rmdir (previous step)

cache_dirs[m] = mkdir(m0, md1, # links(m, cache_dirs), m2, entries0), cache_dirs[entries0[str]] = mkdir(m1, md3, # links(entries0[str], cache_dirs), m4, ∅), afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, c_inode = mkinode(entries0[str], md0, true, # links(entries0[str], cache_dirs), m4, m1), cache_dirs0 = cache_dirs, dent0 = mkdentry(str, entries0[str]), p_inode = mkinode(m, md, true, # links(m, cache_dirs), m2, m0), p_inode0 = mkinode(m, md, true, # links(m, cache_dirs), m2, m0), p_inode1 = mkinode(entries0[str], md0, true, # links(entries0[str], cache_dirs), m4, m1), entries0[str] ≠ ROOT_INO, 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), entries0[str] ∈ cache_dirs, m ∈ cache_dirs, str ∈ entries0, ⌊err0⌋ , cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟨afs_rmdir#(; p_inode0, p_inode1, dent0, err1, cache_dirs, afs_files; afs_asynced)⟩ ( cache_dirs = cache_dirs0 ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ (afs_asynced ↔ asynced) ∧ p_inode = p_inode0 ∧ c_inode = p_inode1 ∧ mkdentry(str, entries0[str]) = dent0 ∧ err0 = err1)

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 280:
cache_dirs[entries0[str]] = mkdir(m1, md3, # links(entries0[str], cache_dirs), m4, ∅), cache_dirs[m] = mkdir(m0, md1, # links(m, cache_dirs), m2, entries0), afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, c_inode = p_inode1, c_inode0 = mkinode(entries0[str], md0, true, # links(entries0[str], cache_dirs), m4, m1), cache_dirs0 = cache_dirs, dent = dent0, dent0 = mkdentry(str, entries0[str]), dirs = cache_dirs, err = err1, files = afs_files, p_inode = p_inode0, p_inode0 = mkinode(m, md, true, # links(m, cache_dirs), m2, m0), p_inode1 = mkinode(entries0[str], md0, true, # links(entries0[str], cache_dirs), m4, m1), p_inode2 = mkinode(m, md, true, # links(m, cache_dirs), m2, m0), 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 ∈ entries0, m ∈ cache_dirs, entries0[str] ∈ cache_dirs, ⌊err0⌋ , cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟨if pre-rmdir(p_inode, c_inode, dent, dirs, files) then { let p_ino = p_inode.ino in {dirs[p_ino].entries := dirs[p_ino].entries -- dent.name; dirs[p_ino].size := dirs[p_ino].size - 1; dirs[p_ino].nsubdirs := dirs[p_ino].nsubdirs - 1; let ino = dent.ino in afs_drop_nlink#(ino; dirs, files); dent := negdentry(dent.name); afs_inode_sync#(p_inode; dirs, files); afs_inode_sync#(c_inode; dirs, files); p_inode := getinode(p_inode.ino, dirs, files); c_inode := getinode(c_inode.ino, dirs, files); err := ESUCCESS} or fail#(; ; err); asynced := ?} else abort⟩ ( dirs = cache_dirs0 ∧ files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ (asynced ↔ asynced0) ∧ p_inode2 = p_inode ∧ c_inode0 = c_inode ∧ mkdentry(str, entries0[str]) = dent ∧ err0 = err), entries0[str] = ROOT_INO

Rule argument

pos: right 1

Additional information

Used simplifier rules: afs_rmdir#(; P_INODE, C_INODE, DENT, ERR, DIRS, FILES; ASYNCED) {if pre-rmdir(P_INODE, C_INODE, DENT, DIRS, FILES) then { let P_INO = P_INODE.ino in {DIRS[P_INO].entries := DIRS[P_INO].entries -- DENT.name; DIRS[P_INO].size := DIRS[P_INO].size - 1; DIRS[P_INO].nsubdirs := DIRS[P_INO].nsubdirs - 1; let INO = DENT.ino in afs_drop_nlink#(INO; DIRS, FILES); DENT := negdentry(DENT.name); afs_inode_sync#(P_INODE; DIRS, FILES); afs_inode_sync#(C_INODE; DIRS, FILES); P_INODE := getinode(P_INODE.ino, DIRS, FILES); C_INODE := getinode(C_INODE.ino, DIRS, FILES); ERR := ESUCCESS} or fail#(; ; ERR); ASYNCED := ?} else abort };