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Proof step 165 from proof inv-link (previous step)

dirs[ino1] = mkdir(m, md, # links(ino1, dirs), m4, entries1), files[entries0[str]] = mkfile(m1, md2, # links(entries0[str], dirs), content0), dirs[ino0] = mkdir(m0, md0, # links(ino0, dirs), m3, entries0), entries0[str] = entries[str], dirs[ino] = mkdir(m2, md1, m5, m6, 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, md, true, # links(ino1, dirs), 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, md), px(user, md0), px(user, md), 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 ∈ 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, entries0[str] ∈ dirs, p.last ∈ entries1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 166:
dirs[ino1] = mkdir(m, md, # links(ino1, dirs), m4, entries1), files[entries[str]] = mkfile(m1, md2, # links(entries[str], dirs), content0), dirs[ino0] = mkdir(m0, md0, # links(ino0, dirs), m3, entries0), entries0[str] = entries[str], dirs[ino] = mkdir(m2, md1, # links(ino, dirs), m6, entries), c_inode = mkinode(entries[str], md2, false, # links(entries[str], dirs), 0, m1), err0 = ESUCCESS, new_dent = negdentry(p.last), new_inode = mkinode(ino1, md, true, # links(ino1, dirs), m4, m), p ≠ ε, 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, md), px(user, md0), px(user, md), px-parent(user, q, ROOT_INO, dirs, files), px-parent(user, parent(p), ROOT_INO, dirs, files), str ∈ entries0, entries[str] ∈ files, ino0 ∈ dirs, ino1 ∈ dirs, ino ∈ dirs, str ∈ entries, ¬ entries[str] ∈ dirs, ¬ p.last ∈ entries1, 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))

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