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Proof step 13 from proof inv-link (previous step)

files[dirs[ino].entries[str]] = mkfile(m0, md1, # links(dirs[ino].entries[str], dirs), content), dirs[m] = mkdir(m1, md2, m2, m4, entries), c_inode = mkinode(dirs[ino].entries[str], md0, false, # links(dirs[ino].entries[str], dirs), 0, m3), new_dent = negdentry(str0), p_inode = mkinode(m, md, true, m2, m4, m1), afs-cons(dirs, files), dirs[ino].entries[str] ∈ files, m ∈ dirs, str ∈ dirs[ino].entries, ino ∈ dirs, links(dirs[ino].entries[str], dirs) ≠ ∅ ∨ dirs[ino].entries[str] = ROOT_INO, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO, links(ino, dirs) ≠ ∅ ∨ ino = ROOT_INO ⊦ ⟪afs_link#(mkdentry(str, dirs[ino].entries[str]); p_inode, c_inode, new_dent, err, dirs, files; asynced)⟫ afs-cons(dirs, files), str0 ∈ entries

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: afs-cons-dir-nlink: ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs ∧ dirs[ino] = mkdir(n0, md, n, n1, entries) → # links(ino, dirs) = n; (forward) from specification afs-base