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Proof step 78 from proof inv-create (previous step)

# links(ino0, dirs) = dirs[ino0].nlink, dirs[ino0] = mkdir(dirs[ino0].size, md0, dirs[ino0].nlink, dirs[ino0].nsubdirs, entries), dent = negdentry(str), err0 = ESUCCESS, inode = mkinode(ino0, md0, true, dirs[ino0].nlink, dirs[ino0].nsubdirs, dirs[ino0].size), afs-cons(dirs, files), ispath(q, ROOT_INO, ino0, dirs, files), of-cons(of, dirs, files), pw(user, md0), px(user, md0), px-parent(user, q, ROOT_INO, dirs, files), ino0 ∈ dirs, ¬ str ∈ dirs[ino0].entries, ¬ str ∈ entries, links(ino0, dirs) ≠ ∅ ∨ ino0 = ROOT_INO ⊦ [afs_create#(md; inode, c_inode, 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 79:
# links(ino0, dirs) = m0, dirs[ino0] = mkdir(m, md0, m0, m1, entries), dirs[ino0] = mkdir(m, md1, m0, m1, entries0), dent = negdentry(str), err0 = ESUCCESS, inode = mkinode(ino0, md0, true, m0, m1, m), afs-cons(dirs, files), ispath(q, ROOT_INO, ino0, dirs, files), of-cons(of, dirs, files), pw(user, md0), px(user, md0), px-parent(user, q, ROOT_INO, dirs, files), ino0 ∈ dirs, links(ino0, dirs) ≠ ∅ ∨ ino0 = ROOT_INO ⊦ [afs_create#(md; inode, c_inode, dent, err0, dirs, files; asynced)] (afs-cons(dirs, files) → of-cons(of, dirs, files)), str ∈ entries0, str ∈ entries

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[ino0], m, md0, m0, m1, entries0]

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[ino0], m, md0, m0, m1, entries0