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Proof step 17 from proof refine-link (previous step)

# links(m, cache_dirs) = m8, cache_dirs[m] = mkdir(m4, md2, # links(m, cache_dirs), m9, entries), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries0[str]] = mkfile(m5, md1, m7, content), cache_dirs[ino] = mkdir(m0, md3, # links(ino, cache_dirs), m2, entries0), afs_dirs = cache_dirs, afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, c_inode = mkinode(entries0[str], md0, false, m7, 0, m6), err = err0, new_dent = negdentry(str0), p_inode = mkinode(m, md, true, # links(m, cache_dirs), m9, m4), 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), ino ∈ cache_dirs, str ∈ entries0, m ∈ cache_dirs, entries0[str] ∈ cache_files, ¬ str0 ∈ entries, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(ino, cache_dirs) ≠ ∅ ∨ ino = ROOT_INO, links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟪cache_link#(mkdentry(str, entries0[str]); p_inode, c_inode, new_dent, err, cache_dirs, cache_files, cache_icache, cache_dcache, cache_asynced)⟫ ⟨old_dent0 := negdentry(str0); p_inode0 := mkinode(m, md, true, m8, m9, m4); p_inode1 := mkinode(entries0[str], md0, false, m7, 0, m6); afs_link#(mkdentry(str, entries0[str]); p_inode0, p_inode1, old_dent0, err0, afs_dirs, afs_files; afs_asynced)⟩ ( afs_dirs = cache_dirs ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ (afs_asynced ↔ cache_asynced) ∧ p_inode = p_inode0 ∧ c_inode = p_inode1 ∧ new_dent = old_dent0 ∧ err = err0)

User applied rule call right

And obtained the following new goals

Proof step 18:
# links(m, cache_dirs) = m8, asynced0 ↔ cache_asynced, cache_dirs[ino] = mkdir(m0, md3, # links(ino, cache_dirs), m2, entries0), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries0[str]] = mkfile(m5, md1, m7, content), cache_dirs[m] = mkdir(m4, md2, # links(m, cache_dirs), m9, entries), afs_dirs = cache_dirs, afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, c_inode = mkinode(entries0[str], md0, false, m7, 0, m6), dcache = cache_dcache, dirs = cache_dirs, err = err0, files = cache_files, icache = cache_icache, new_dent = negdentry(str0), old_dent = mkdentry(str, entries0[str]), p_inode = mkinode(m, md, true, # links(m, cache_dirs), m9, m4), 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), entries0[str] ∈ cache_files, m ∈ cache_dirs, str ∈ entries0, ino ∈ cache_dirs, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO, links(ino, cache_dirs) ≠ ∅ ∨ ino = ROOT_INO ⊦ ⟪if pre-link(p_inode, c_inode, old_dent, new_dent, dirs, files) then {afs_link#(old_dent; p_inode, c_inode, new_dent, err, dirs, files; asynced0); if err = ESUCCESS then let asynced = false in {icache_set#(p_inode, asynced; err, icache); icache_set#(c_inode, asynced; err, icache); dcache_set#(p_inode.ino, new_dent.name, new_dent; err, dcache)}} else abort⟫ ⟨old_dent0 := negdentry(str0); p_inode0 := mkinode(m, md, true, m8, m9, m4); p_inode1 := mkinode(entries0[str], md0, false, m7, 0, m6); afs_link#(mkdentry(str, entries0[str]); p_inode0, p_inode1, old_dent0, err0, afs_dirs, afs_files; afs_asynced)⟩ ( afs_dirs = dirs ∧ afs_files = (files ⊕ cache_pcache) ⊕ icache ∧ (afs_asynced ↔ asynced0) ∧ p_inode = p_inode0 ∧ c_inode = p_inode1 ∧ new_dent = old_dent0 ∧ err = err0), str0 ∈ entries

Rule argument

pos: right 1

Additional information

Used simplifier rules: cache_link# (OLD_DENT ; P_INODE, C_INODE, NEW_DENT, ERR, DIRS, FILES, ICACHE, DCACHE, ASYNCED ) {if pre-link(P_INODE, C_INODE, OLD_DENT, NEW_DENT, DIRS, FILES) then {afs_link# (OLD_DENT ; P_INODE, C_INODE, NEW_DENT, ERR, DIRS, FILES ; ASYNCED); if ERR = ESUCCESS then let DIRTY = false in {icache_set#(P_INODE, DIRTY; ERR, ICACHE); icache_set#(C_INODE, DIRTY; ERR, ICACHE); dcache_set# (P_INODE.ino, NEW_DENT.name, NEW_DENT; ERR, DCACHE)}} else abort };