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Proof step 206 from proof inv-unlink (previous step)

# links(ino1, dirs) = dirs[ino1].nlink, entries0[str] = dirs[ino1].entries[str], dirs[ino1] = mkdir(dirs[ino1].size, md0, dirs[ino1].nlink, dirs[ino1].nsubdirs, entries0), files[entries0[str]] = mkfile(m0, md, # links(entries0[str], dirs), content), dom of < ino0, afs-cons(dirs, files), ispath(q, ROOT_INO, ino1, dirs, files), of-cons(of, dirs, files), pw(user, md0), px(user, md0), px-parent(user, q, ROOT_INO, dirs, files), str ∈ dirs[ino1].entries, str ∈ entries0, entries0[str] ∈ files, ino1 ∈ dirs, ¬ entries0[str] ∈ dirs, links(ino1, dirs) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ [fail#(; ; err); asynced := ?] ⟪vfs_put_inode#(mkinode(entries0[str], md, false, # links(entries0[str], dirs), 0, m0), 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 207:
# links(ino1, dirs) = m1, files[entries0[str]] = mkfile(m0, md, # links(entries0[str], dirs), content), dirs[ino1] = mkdir(m, md0, m1, m2, entries0), entries0[str] = entries[str], dirs[ino1] = mkdir(m, md1, m1, m2, entries), dom of < ino0, afs-cons(dirs, files), ispath(q, ROOT_INO, ino1, dirs, files), of-cons(of, dirs, files), pw(user, md0), px(user, md0), px-parent(user, q, ROOT_INO, dirs, files), ino1 ∈ dirs, entries0[str] ∈ files, str ∈ entries0, str ∈ entries, links(ino1, dirs) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ [fail#(; ; err); asynced := ?] ⟪vfs_put_inode#(mkinode(entries0[str], md, false, # links(entries0[str], dirs), 0, m0), of, asynced; err, dirs, files)⟫ (of-cons(of, dirs, files) ∧ afs-cons(dirs, files)), entries0[str] ∈ dirs

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[ino1], m, 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[ino1], m, md1, m1, m2, entries