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Proof step 8 from proof inv-rmdir (previous step)

dirs[dirs[m].entries[str]].entries = ∅, c_inode = mkinode(dirs[m].entries[str], md, true, dirs[dirs[m].entries[str]].nlink, dirs[dirs[m].entries[str]].nsubdirs, dirs[dirs[m].entries[str]].size), dent = mkdentry(str, dirs[m].entries[str]), p_inode = mkinode(m, md0, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size), dirs[m].entries[str] ≠ ROOT_INO, afs-cons(dirs, files), dirs[m].entries[str] ∈ dirs, str ∈ dirs[m].entries, m ∈ dirs, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟪afs_rmdir#(; p_inode, c_inode, dent, err, dirs, files; asynced)⟫ afs-cons(dirs, files)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 9:
dirs[dirs[m].entries[str]] = mkdir(m0, md1, m1, m2, entries), c_inode = mkinode(dirs[m].entries[str], md, true, m1, m2, m0), dent = mkdentry(str, dirs[m].entries[str]), entries = ∅, p_inode = mkinode(m, md0, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size), afs-cons(dirs, files), m ∈ dirs, str ∈ dirs[m].entries, dirs[m].entries[str] ∈ dirs, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟪afs_rmdir#(; p_inode, c_inode, dent, err, dirs, files; asynced)⟫ afs-cons(dirs, files), dirs[m].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[dirs[m].entries[str]], m0, md1, m1, m2, entries]

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[dirs[m].entries[str]], m0, md1, m1, m2, entries