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Proof step 30 from proof inv-link (previous step)

dirs[ino0] = mkdir(m2, md1, # links(ino0, dirs), m8, entries), entries0[str] = entries[str], files[entries[str]] = mkfile(m0, md4, # links(entries[str], dirs), content0), dirs[m] = mkdir(m1, md2, # links(m, dirs), m5, entries1), dirs[ino] = mkdir(m4, md3, # links(ino, dirs), m6, entries0), c_inode = mkinode(entries[str], md0, false, # links(entries[str], dirs), 0, m3), new_dent = negdentry(str0), old_dent0 = mkdentry(str, entries0[str]), p_inode = mkinode(m, md, true, # links(m, dirs), m5, m1), afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), pre-link(p_inode, c_inode, mkdentry(str, entries0[str]), new_dent, dirs, files), synced(dirs, icache, pcache), str ∈ entries, ino0 ∈ dirs, ino ∈ dirs, str ∈ entries0, m ∈ dirs, entries[str] ∈ files, asynced → synced(files, icache, pcache), 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)) ∧ afs-cons(dirs, files))), str0 ∈ entries1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 31:
# 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))))

Rule argument

Additional information

Used simplifier rules: afs-cons-file-nlink: ⊦ afs-cons(dirs, files) ∧ ino ∈ files ∧ files[ino] = mkfile(m, md, n, content) → # links(ino, dirs) = n; (forward) from specification afs-base% ⊦ valid-file-ino(ino, dirs, files) ↔ ino ∈ files; (s)%⊦ valid-file-inode(inode, dirs, files) ↔ valid-file-ino(inode.ino, dirs, files) ∧ inode.nlink = files[inode.ino].nlink ∧ inode.nsubdirs = 0 ∧ ¬ inode.directory; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).directory ↔ boolvar; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nsubdirs = m1; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).size = m2; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nlink = m0; (s)% ⊦ valid-dir-ino(ino, dirs, files) ↔ ino ∈ dirs; (s)%⊦ valid-dir-inode(inode, dirs, files) ↔ valid-dir-ino(inode.ino, dirs, files) ∧ inode.nlink = dirs[inode.ino].nlink ∧ inode.size = dirs[inode.ino].size ∧ inode.nsubdirs = dirs[inode.ino].nsubdirs ∧ inode.directory; (s)%⊦ p_ino ∈ dirs ∧ dirs[p_ino] = mkdir(m, md, n, n0, entries) ∧ str ∈ entries → links(entries[str], dirs) ≠ ∅; (s)% ⊦ negdentry(str).negdentry?; (s)% ⊦ negdentry(str).name = str; (s)%⊦ valid-negdentry(ino, dent, dirs, files) ↔ valid-parent-ino(ino, dirs, files) ∧ ¬ dent.name ∈ dirs[ino].entries ∧ dent.negdentry?; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)% ⊦ mkdentry(str, m).dentry?; (s)% ⊦ mkdentry(str, m).name = str; (s)% ⊦ valid-ino(ino, dirs, files) ↔ ino ∈ dirs ∨ ino ∈ files; (s)% ⊦ mkdentry(str, m).ino = m; (s)%⊦ valid-parent-ino(ino, dirs, files) ↔ ino ∈ dirs ∧ (links(ino, dirs) ≠ ∅ ∨ ino = ROOT_INO); (s)%⊦ valid-dentry(ino, dent, dirs, files) ↔ valid-parent-ino(ino, dirs, files) ∧ valid-ino(dent.ino, dirs, files) ∧ dent.name ∈ dirs[ino].entries ∧ dent.ino = dirs[ino].entries[dent.name] ∧ dent.dentry?; (s)%⊦ valid-dentry(dent, dirs, files) ↔ (∃ ino. valid-dentry(ino, dent, dirs, files)); (s)%⊦ pre-link(p_inode, c_inode, old_dent, new_dent, dirs, files) ↔ valid-dentry(old_dent, dirs, files) ∧ valid-negdentry(p_inode.ino, new_dent, dirs, files) ∧ (links(old_dent.ino, dirs) ≠ ∅ ∨ old_dent.ino = ROOT_INO) ∧ valid-dir-inode(p_inode, dirs, files) ∧ valid-file-inode(c_inode, dirs, files) ∧ c_inode.ino = old_dent.ino; (s)