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Proof step 31 from proof inv-link (previous step)

# links(entries[str], dirs) = files[entries[str]].nlink, # links(m, dirs) = dirs[m].nlink, entries[str] = dirs[ino1].entries[str], dirs[ino0] = mkdir(m2, md1, # links(ino0, dirs), m8, entries), entries0[str] = entries[str], files[entries[str]] = mkfile(m0, md4, files[entries[str]].nlink, content0), dirs[m] = mkdir(dirs[m].size, md2, dirs[m].nlink, dirs[m].nsubdirs, entries1), dirs[ino] = mkdir(m4, md3, # links(ino, dirs), m6, entries0), c_inode = mkinode(entries[str], md0, false, files[entries[str]].nlink, 0, m3), new_dent = negdentry(str0), p_inode = mkinode(m, md, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size), afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), str ∈ dirs[ino1].entries, ino1 ∈ dirs, str ∈ entries, ino0 ∈ dirs, ino ∈ dirs, str ∈ entries0, m ∈ dirs, entries[str] ∈ files, ¬ str0 ∈ dirs[m].entries, ¬ str0 ∈ entries1, asynced → synced(files, icache, pcache), links(ino1, dirs) ≠ ∅ ∨ ino1 = ROOT_INO, links(ino0, dirs) ≠ ∅ ∨ ino0 = ROOT_INO, links(ino, dirs) ≠ ∅ ∨ ino = ROOT_INO, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ [afs_link#(mkdentry(str, entries0[str]); p_inode, c_inode, new_dent, err, dirs, files; asynced0)] ( afs-cons(dirs, files) → ⟪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)}⟫ ( icache-cons(icache, dirs, files) ∧ dcache-cons(dcache, dirs, files) ∧ pcache-cons(pcache, dirs, files) ∧ synced(dirs, icache, pcache) ∧ (asynced → synced(files, icache, pcache))))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 32:
# links(m, dirs) = dirs[m].nlink, # links(entries[str], dirs) = m5, dirs[ino] = mkdir(m4, md3, # links(ino, dirs), m6, entries0), dirs[m] = mkdir(dirs[m].size, md2, dirs[m].nlink, dirs[m].nsubdirs, entries1), files[entries[str]] = mkfile(m0, md4, m5, content0), entries0[str] = entries[str], dirs[ino0] = mkdir(m2, md1, # links(ino0, dirs), m8, entries), entries[str] = dirs[ino1].entries[str], files[entries[str]] = mkfile(m1, md5, m5, content), c_inode = mkinode(entries[str], md0, false, m5, 0, m3), new_dent = negdentry(str0), p_inode = mkinode(m, md, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size), afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), entries[str] ∈ files, m ∈ dirs, str ∈ entries0, ino ∈ dirs, ino0 ∈ dirs, str ∈ entries, ino1 ∈ dirs, str ∈ dirs[ino1].entries, asynced → synced(files, icache, pcache), links(m, dirs) ≠ ∅ ∨ m = ROOT_INO, links(ino, dirs) ≠ ∅ ∨ ino = ROOT_INO, links(ino0, dirs) ≠ ∅ ∨ ino0 = ROOT_INO, links(ino1, dirs) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ [afs_link#(mkdentry(str, entries0[str]); p_inode, c_inode, new_dent, err, dirs, files; asynced0)] ( afs-cons(dirs, files) → ⟪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)}⟫ ( icache-cons(icache, dirs, files) ∧ dcache-cons(dcache, dirs, files) ∧ pcache-cons(pcache, dirs, files) ∧ synced(dirs, icache, pcache) ∧ (asynced → synced(files, icache, pcache)))), str0 ∈ dirs[m].entries, str0 ∈ entries1

Rule argument

spec: abstract-file name: elim seq: ⊦ ((m = af.size ∧ md = af.meta) ∧ m0 = af.nlink) ∧ content = af.content ↔ af = mkfile(m, md, m0, content) subst: [af, m, md, m0, content] → [files[entries[str]], m1, md5, m5, content]

Additional information

Used simplifier rules: ⊦ ((m = af.size ∧ md = af.meta) ∧ m0 = af.nlink) ∧ content = af.content ↔ af = mkfile(m, md, m0, content); (elim) Used terms: files[entries[str]], m1, md5, m5, content