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Proof step 278 from proof refine-link (previous step)

cache_dirs[ino1] = mkdir(m7, md5, # links(ino1, cache_dirs), m11, entries1), entries[str] = entries1[str], cache_dirs[ino0] = mkdir(m4, md2, # links(ino0, cache_dirs), m10, entries), cache_dirs[ino] = mkdir(m0, md3, # links(ino, cache_dirs), m2, entries0), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries1[str]] = mkfile(m5, md1, # links(entries1[str], cache_dirs), content), cache_dirs[m] = mkdir(m1, md4, # links(m, cache_dirs), m8, entries2), entries0[str] = entries1[str], cache_files[entries1[str]] = mkfile(m3, md6, # links(entries1[str], cache_dirs), content1), afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, c_inode = mkinode(entries1[str], md0, false, # links(entries1[str], cache_dirs), 0, m6), cache_dirs0 = cache_dirs, old_dent0 = negdentry(str0), p_inode = mkinode(m, md, true, # links(m, cache_dirs), m8, m1), p_inode0 = mkinode(m, md, true, # links(m, cache_dirs), m8, m1), p_inode1 = mkinode(entries1[str], md0, false, # links(entries1[str], cache_dirs), 0, m6), 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 ∈ entries1, ino1 ∈ cache_dirs, entries1[str] ∈ cache_files, m ∈ cache_dirs, ino ∈ cache_dirs, ino0 ∈ cache_dirs, str ∈ entries0, str ∈ entries, ⌊err0⌋ , ¬ str0 ∈ entries2, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(ino1, cache_dirs) ≠ ∅ ∨ ino1 = ROOT_INO, links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO, links(ino, cache_dirs) ≠ ∅ ∨ ino = ROOT_INO, links(ino0, cache_dirs) ≠ ∅ ∨ ino0 = ROOT_INO ⊦ ⟨afs_link#(mkdentry(str, entries0[str]); p_inode0, p_inode1, old_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 ∧ negdentry(str0) = old_dent0 ∧ err0 = err1)

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 279:
cache_files[entries1[str]] = mkfile(m3, md6, # links(entries1[str], cache_dirs), content1), entries0[str] = entries1[str], cache_dirs[m] = mkdir(m1, md4, # links(m, cache_dirs), m8, entries2), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries1[str]] = mkfile(m5, md1, # links(entries1[str], cache_dirs), content), cache_dirs[ino] = mkdir(m0, md3, # links(ino, cache_dirs), m2, entries0), cache_dirs[ino0] = mkdir(m4, md2, # links(ino0, cache_dirs), m10, entries), entries[str] = entries1[str], cache_dirs[ino1] = mkdir(m7, md5, # links(ino1, cache_dirs), m11, entries1), afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, c_inode = p_inode1, c_inode0 = mkinode(entries1[str], md0, false, # links(entries1[str], cache_dirs), 0, m6), cache_dirs0 = cache_dirs, dirs = cache_dirs, err = err1, files = afs_files, new_dent = old_dent0, old_dent = mkdentry(str, entries0[str]), old_dent0 = negdentry(str0), p_inode = p_inode0, p_inode0 = mkinode(m, md, true, # links(m, cache_dirs), m8, m1), p_inode1 = mkinode(entries1[str], md0, false, # links(entries1[str], cache_dirs), 0, m6), p_inode2 = mkinode(m, md, true, # links(m, cache_dirs), m8, m1), 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, str ∈ entries0, ino0 ∈ cache_dirs, ino ∈ cache_dirs, m ∈ cache_dirs, entries1[str] ∈ cache_files, ino1 ∈ cache_dirs, str ∈ entries1, ⌊err0⌋ , cache_sync → synced(cache_files, cache_icache, cache_pcache), links(ino0, cache_dirs) ≠ ∅ ∨ ino0 = ROOT_INO, links(ino, cache_dirs) ≠ ∅ ∨ ino = ROOT_INO, links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO, links(ino1, cache_dirs) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ ⟨if pre-link(p_inode, c_inode, old_dent, new_dent, dirs, files) then { let p_ino = p_inode.ino in {dirs[p_ino].entries[new_dent.name] := old_dent.ino; dirs[p_ino].size := dirs[p_ino].size + 1; let ino = old_dent.ino in afs_inc_nlink#(ino; dirs, files); new_dent := mkdentry(new_dent.name, old_dent.ino); 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(old_dent.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 ∧ negdentry(str0) = new_dent ∧ err0 = err), str0 ∈ entries2

Rule argument

pos: right 1

Additional information

Used simplifier rules: afs_link# (OLD_DENT; P_INODE, C_INODE, NEW_DENT, ERR, DIRS, FILES; ASYNCED) {if pre-link(P_INODE, C_INODE, OLD_DENT, NEW_DENT, DIRS, FILES) then { let P_INO = P_INODE.ino in {DIRS[P_INO].entries[NEW_DENT.name] := OLD_DENT.ino; DIRS[P_INO].size := DIRS[P_INO].size + 1; let INO = OLD_DENT.ino in afs_inc_nlink#(INO; DIRS, FILES); NEW_DENT := mkdentry(NEW_DENT.name, OLD_DENT.ino); 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(OLD_DENT.ino, DIRS, FILES); ERR := ESUCCESS} or fail#(; ; ERR); ASYNCED := ?} else abort };