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Proof step 285 from proof refine-link (previous step)

# entries = dirs0[ino2].size, # links(ino2, dirs0) = dirs0[ino2].nlink, entries0[str] = dirs0[ino].entries[str], dirs0[ino1] = mkdir(# entries0, md0, # links(ino1, dirs0), m2, entries0), files[entries0[str]] = mkfile(m0, md2, # links(entries0[str], dirs0), content0), dirs0[ino2] = mkdir(# entries, md1, dirs0[ino2].nlink, dirs0[ino2].nsubdirs, entries), fs = abs-files(files), root[q0].dir?, root[q].dir?, root.dir?, dom of < ino0, abs(root, ROOT_INO)(dirs0), afs-cons(dirs0, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(q, ROOT_INO, ino1, dirs0, files), ispath(q0, ROOT_INO, ino2, dirs0, files), of-cons(of, dirs0, files), pw(user, md1), px(user, md1), px(user, md0), px-parent(user, q, ROOT_INO, dirs0, files), px-parent(user, q0, ROOT_INO, dirs0, files), str ∈ dirs0[ino].entries, ino ∈ dirs0, ino2 ∈ dirs0, ino1 ∈ dirs0, entries0[str] ∈ files, str ∈ entries0, dirs ≡ dirs0[ino2, (dirs0[ino2].entries:= dirs0[ino2].entries[str0, entries0[str]]).size:= (# entries + 1)], ¬ root[q + str '].dir?, ¬ entries0[str] ∈ dirs, ¬ str0 ∈ entries, ¬ entries0[str] ∈ dirs0, ¬ str0 ∈ dirs0[ino2].entries, psynced → asynced0, links(ino, dirs0) ≠ ∅ ∨ ino = ROOT_INO, links(ino2, dirs0) ≠ ∅ ∨ ino2 = ROOT_INO, links(ino1, dirs0) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ [afs_inc_nlink#(mkdentry(str, entries0[str]).ino; dirs, files); new_dent := mkdentry(str0, mkdentry(str, entries0[str]).ino); afs_inode_sync#(mkinode(ino2, md1, true, dirs0[ino2].nlink, dirs0[ino2].nsubdirs, # entries); dirs, files); afs_inode_sync#(mkinode(entries0[str], md2, false, # links(entries0[str], dirs0), 0, m0); dirs, files); new_inode := (ino2 ∈ dirs ⊃ mkinode(ino2, dirs[ino2].meta, true, dirs[ino2].nlink, dirs[ino2].nsubdirs, dirs[ino2].size) ;mkinode(ino2, files[ino2].meta, false, files[ino2].nlink, 0, files[ino2].size) ); c_inode := getinode(mkdentry(str, entries0[str]).ino, dirs, files); err := ESUCCESS; asynced := ?] ( of-cons(of, dirs, files) ∧ afs-cons(dirs, files) → ⟨posix_link#(q + str ', q0 + str0 ', user, fs, abs-of(of); err2, root; psynced)⟩ (fs = abs-files(files) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ err = err2))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 286:
# links(ino2, dirs0) = m1, # entries = m, dirs0[ino2] = mkdir(# entries, md1, m1, m3, entries), files[entries0[str]] = mkfile(m0, md2, # links(entries0[str], dirs0), content0), dirs0[ino1] = mkdir(# entries0, md0, # links(ino1, dirs0), m2, entries0), entries0[str] = dirs0[ino].entries[str], dirs0[ino2] = mkdir(m, md, m1, m3, entries1), fs = abs-files(files), root.dir?, root[q].dir?, root[q0].dir?, dom of < ino0, abs(root, ROOT_INO)(dirs0), afs-cons(dirs0, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(q0, ROOT_INO, ino2, dirs0, files), ispath(q, ROOT_INO, ino1, dirs0, files), of-cons(of, dirs0, files), pw(user, md1), px(user, md0), px(user, md1), px-parent(user, q0, ROOT_INO, dirs0, files), px-parent(user, q, ROOT_INO, dirs0, files), str ∈ entries0, entries0[str] ∈ files, ino1 ∈ dirs0, ino2 ∈ dirs0, ino ∈ dirs0, str ∈ dirs0[ino].entries, dirs ≡ dirs0[ino2, (dirs0[ino2].entries:= entries1[str0, entries0[str]]).size:= (# entries + 1)], psynced → asynced0, links(ino1, dirs0) ≠ ∅ ∨ ino1 = ROOT_INO, links(ino2, dirs0) ≠ ∅ ∨ ino2 = ROOT_INO, links(ino, dirs0) ≠ ∅ ∨ ino = ROOT_INO ⊦ [afs_inc_nlink#(mkdentry(str, entries0[str]).ino; dirs, files); new_dent := mkdentry(str0, mkdentry(str, entries0[str]).ino); afs_inode_sync#(mkinode(ino2, md1, true, m1, m3, # entries); dirs, files); afs_inode_sync#(mkinode(entries0[str], md2, false, # links(entries0[str], dirs0), 0, m0); dirs, files); new_inode := (ino2 ∈ dirs ⊃ mkinode(ino2, dirs[ino2].meta, true, dirs[ino2].nlink, dirs[ino2].nsubdirs, dirs[ino2].size) ;mkinode(ino2, files[ino2].meta, false, files[ino2].nlink, 0, files[ino2].size) ); c_inode := getinode(mkdentry(str, entries0[str]).ino, dirs, files); err := ESUCCESS; asynced := ?] ( of-cons(of, dirs, files) ∧ afs-cons(dirs, files) → ⟨posix_link#(q + str ', q0 + str0 ', user, fs, abs-of(of); err2, root; psynced)⟩ (fs = abs-files(files) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ err = err2)), root[q + str '].dir?, entries0[str] ∈ dirs, str0 ∈ entries, entries0[str] ∈ dirs0, str0 ∈ entries1

Rule argument

spec: abstract-dir name: elim seq: ⊦ ( ((m = ad.size ∧ md = ad.meta) ∧ m0 = ad.nlink) ∧ m1 = ad.nsubdirs) ∧ entries = ad.entries ↔ ad = mkdir(m, md, m0, m1, entries) subst: [ad, m, md, m0, m1, entries] → [dirs0[ino2], m, md, m1, m3, entries1]

Additional information

Used simplifier rules: ⊦ ( ((m = ad.size ∧ md = ad.meta) ∧ m0 = ad.nlink) ∧ m1 = ad.nsubdirs) ∧ entries = ad.entries ↔ ad = mkdir(m, md, m0, m1, entries); (elim) Used terms: dirs0[ino2], m, md, m1, m3, entries1