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Proof step 162 from proof inv-link (previous step)

# links(ino1, dirs) = dirs[ino1].nlink, entries0[str] = dirs[ino].entries[str], dirs[ino0] = mkdir(m0, md0, # links(ino0, dirs), m3, entries0), files[entries0[str]] = mkfile(m1, md2, # links(entries0[str], dirs), content0), dirs[ino1] = mkdir(dirs[ino1].size, md1, dirs[ino1].nlink, dirs[ino1].nsubdirs, entries), c_inode = mkinode(entries0[str], md2, false, # links(entries0[str], dirs), 0, m1), err0 = ESUCCESS, new_dent = negdentry(p.last), new_inode = mkinode(ino1, md1, true, dirs[ino1].nlink, dirs[ino1].nsubdirs, dirs[ino1].size), p ≠ ε, afs-cons(dirs, files), ispath(parent(p), ROOT_INO, ino1, dirs, files), ispath(q, ROOT_INO, ino0, dirs, files), of-cons(of, dirs, files), pw(user, md1), px(user, md1), px(user, md0), px-parent(user, parent(p), ROOT_INO, dirs, files), px-parent(user, q, ROOT_INO, dirs, files), str ∈ dirs[ino].entries, ino ∈ dirs, ino1 ∈ dirs, ino0 ∈ dirs, entries0[str] ∈ files, str ∈ entries0, ¬ p.last ∈ entries, ¬ entries0[str] ∈ dirs, ¬ p.last ∈ dirs[ino1].entries, links(ino, dirs) ≠ ∅ ∨ ino = ROOT_INO, links(ino1, dirs) ≠ ∅ ∨ ino1 = ROOT_INO, links(ino0, dirs) ≠ ∅ ∨ ino0 = ROOT_INO ⊦ [afs_link#(mkdentry(str, entries0[str]); new_inode, c_inode, new_dent, err0, dirs, files; asynced)] (afs-cons(dirs, files) → of-cons(of, dirs, files))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 163:
# links(ino1, dirs) = m2, dirs[ino1] = mkdir(m, md1, m2, m4, entries), files[entries0[str]] = mkfile(m1, md2, # links(entries0[str], dirs), content0), dirs[ino0] = mkdir(m0, md0, # links(ino0, dirs), m3, entries0), entries0[str] = dirs[ino].entries[str], dirs[ino1] = mkdir(m, md, m2, m4, entries1), c_inode = mkinode(entries0[str], md2, false, # links(entries0[str], dirs), 0, m1), err0 = ESUCCESS, new_dent = negdentry(p.last), new_inode = mkinode(ino1, md1, true, m2, m4, m), afs-cons(dirs, files), ispath(q, ROOT_INO, ino0, dirs, files), ispath(parent(p), ROOT_INO, ino1, dirs, files), of-cons(of, dirs, files), pw(user, md1), px(user, md0), px(user, md1), px-parent(user, q, ROOT_INO, dirs, files), px-parent(user, parent(p), ROOT_INO, dirs, files), str ∈ entries0, entries0[str] ∈ files, ino0 ∈ dirs, ino1 ∈ dirs, ino ∈ dirs, str ∈ dirs[ino].entries, links(ino0, dirs) ≠ ∅ ∨ ino0 = ROOT_INO, links(ino1, dirs) ≠ ∅ ∨ ino1 = ROOT_INO, links(ino, dirs) ≠ ∅ ∨ ino = ROOT_INO ⊦ [afs_link#(mkdentry(str, entries0[str]); new_inode, c_inode, new_dent, err0, dirs, files; asynced)] (afs-cons(dirs, files) → of-cons(of, dirs, files)), p = ε, p.last ∈ entries, entries0[str] ∈ dirs, p.last ∈ 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] → [dirs[ino1], m, md, m2, m4, 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[ino1], m, md, m2, m4, entries1