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Proof step 130 from proof inv-rmdir (previous step)

# links(entries[str], dirs) = dirs[entries[str]].nlink, # links(ino1, dirs) = dirs[ino1].nlink, dirs[entries[str]].entries = ∅, 0 = dirs[entries[str]].size, entries[str] = dirs[ino1].entries[str], dirs[entries[str]] = mkdir(0, md0, dirs[entries[str]].nlink, dirs[entries[str]].nsubdirs, entries0), dirs[ino1] = mkdir(dirs[ino1].size, md, dirs[ino1].nlink, dirs[ino1].nsubdirs, entries), dent = mkdentry(str, entries[str]), err = ESUCCESS, inode = mkinode(ino1, md, true, dirs[ino1].nlink, dirs[ino1].nsubdirs, dirs[ino1].size), p_inode = mkinode(entries[str], md0, true, dirs[entries[str]].nlink, dirs[entries[str]].nsubdirs, 0), entries[str] ≠ ROOT_INO, dom of < ino0, afs-cons(dirs, files), ispath(q, ROOT_INO, ino1, dirs, files), of-cons(of, dirs, files), pw(user, md), px(user, md), px-parent(user, q, ROOT_INO, dirs, files), str ∈ dirs[ino1].entries, str ∈ entries, ino1 ∈ dirs, entries[str] ∈ dirs, links(ino1, dirs) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ [afs_rmdir#(; inode, p_inode, dent, err, dirs, files; asynced)] (afs-cons(dirs, files) → ⟪vfs_put_inode#(p_inode, of, asynced; err, dirs, files)⟫ (of-cons(of, dirs, files) ∧ afs-cons(dirs, files)))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 131:
# links(ino1, dirs) = dirs[ino1].nlink, # links(entries[str], dirs) = m0, 0 = m, dirs[ino1] = mkdir(dirs[ino1].size, md, dirs[ino1].nlink, dirs[ino1].nsubdirs, entries), dirs[entries[str]] = mkdir(0, md0, m0, m1, entries0), entries[str] = dirs[ino1].entries[str], dirs[entries[str]] = mkdir(m, md1, m0, m1, entries1), dent = mkdentry(str, entries[str]), entries1 = ∅, err = ESUCCESS, inode = mkinode(ino1, md, true, dirs[ino1].nlink, dirs[ino1].nsubdirs, dirs[ino1].size), p_inode = mkinode(entries[str], md0, true, m0, m1, 0), dom of < ino0, afs-cons(dirs, files), ispath(q, ROOT_INO, ino1, dirs, files), of-cons(of, dirs, files), pw(user, md), px(user, md), px-parent(user, q, ROOT_INO, dirs, files), entries[str] ∈ dirs, ino1 ∈ dirs, str ∈ entries, str ∈ dirs[ino1].entries, links(ino1, dirs) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ [afs_rmdir#(; inode, p_inode, dent, err, dirs, files; asynced)] (afs-cons(dirs, files) → ⟪vfs_put_inode#(p_inode, of, asynced; err, dirs, files)⟫ (of-cons(of, dirs, files) ∧ afs-cons(dirs, files))), entries[str] = ROOT_INO

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] → [dirs[entries[str]], m, md, m0, m1, 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: dirs[entries[str]], m, md, m0, m1, entries1