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Proof step 19 from proof abs-acyclic (previous step)

dirs[ino] = mkdir(# entries, md, # links(ino, dirs), m0, entries), entries[str] = ROOT_INO, tree[p] = dnode(md0, sdt), (((ino0 => mkdir(# entries0, md0, m1, m2, entries0) * abs(sdt, entries0)) * abs|(tree, ROOT_INO, p, ino0)))(dirs), abs(tree, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(tree, abs-files(files), ofh), ispath(p, ROOT_INO, ino, dirs, files), str ∈ entries, ino ∈ dirs ⊦

User applied rule apply lemma

And obtained the following new goals

Proof step 20:
⊦ p ∈ tree ∧ ((abs|(tree, ino, p, ino0) * D))(dirs) ∧ ispath(p, ino, ino1, dirs, files) → ino0 = ino1
Proof step 21:
tree[p] = dnode(md0, sdt), entries[str] = ROOT_INO, dirs[ino] = mkdir(# entries, md, # links(ino, dirs), m0, entries), (((ino0 => mkdir(# entries0, md0, m1, m2, entries0) * abs(sdt, entries0)) * abs|(tree, ROOT_INO, p, ino0)))(dirs), abs(tree, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(tree, abs-files(files), ofh), ispath(p, ROOT_INO, ino, dirs, files), ino ∈ dirs, str ∈ entries, p ∈ tree ∧ ((abs|(tree, ROOT_INO, p, ino0) * abs(sdt, entries0) * ino0 => mkdir(# entries0, md0, m1, m2, entries0)))(dirs) ∧ ispath(p, ROOT_INO, ino, dirs, files) → ino0 = ino ⊦

Rule argument

spec: vfs-abs name: absc-path seq: ⊦ p ∈ tree ∧ ((abs|(tree, ino, p, ino0) * D))(dirs) ∧ ispath(p, ino, ino1, dirs, files) → ino0 = ino1 subst: [p, tree, ino, ino0, D, dirs, ino1, files] → [p, tree, ROOT_INO, ino0, abs(sdt, entries0) * ino0 => mkdir(# entries0, md0, m1, m2, entries0), dirs, ino, files]

Additional information

Used terms: p, tree, ROOT_INO, ino0, abs(sdt, entries0) * ino0 => mkdir(# entries0, md0, m1, m2, entries0), dirs, ino, files