[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 9 from proof refine-create (previous step)

# links(m, cache_dirs) = m4, cache_dirs[m] = mkdir(m3, md1, # links(m, cache_dirs), m5, entries), afs_dirs = cache_dirs, afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, c_inode = p_inode1, dent = negdentry(str), err = err0, p_inode = mkinode(m, md0, true, # links(m, cache_dirs), m5, m3), 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), m ∈ cache_dirs, ¬ str ∈ entries, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟪cache_create#(md; p_inode, c_inode, dent, err, cache_dirs, cache_files, cache_icache, cache_dcache, cache_asynced)⟫ ⟨dent0 := negdentry(str); p_inode0 := mkinode(m, md0, true, m4, m5, m3); afs_create#(md; p_inode0, p_inode1, 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 ∧ dent = dent0 ∧ err = err0)

User applied rule call right

And obtained the following new goals

Proof step 10:
# links(m, cache_dirs) = m4, asynced0 ↔ cache_asynced, cache_dirs[m] = mkdir(m3, md1, # links(m, cache_dirs), m5, entries), afs_dirs = cache_dirs, afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, c_inode = p_inode1, dcache = cache_dcache, dent = negdentry(str), dirs = cache_dirs, err = err0, files = cache_files, icache = cache_icache, p_inode = mkinode(m, md0, true, # links(m, cache_dirs), m5, m3), 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), m ∈ cache_dirs, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟪if pre-create(p_inode, dent, md, dirs, files) then {afs_create#(md; p_inode, c_inode, 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, dent.name, dent; err, dcache)}} else abort⟫ ⟨dent0 := negdentry(str); p_inode0 := mkinode(m, md0, true, m4, m5, m3); afs_create#(md; p_inode0, p_inode1, 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 ∧ dent = dent0 ∧ err = err0), str ∈ entries

Rule argument

pos: right 1

Additional information

Used simplifier rules: cache_create# (MD; P_INODE, C_INODE, DENT, ERR, DIRS, FILES, ICACHE, DCACHE, ASYNCED ) {if pre-create(P_INODE, DENT, MD, DIRS, FILES) then {afs_create# (MD; P_INODE, C_INODE, 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, DENT.name, DENT; ERR, DCACHE)}} else abort };