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Proof step 10 from proof path-links-empty (previous step)

links(n, dirs) = ∅, ispath(p0 + str ', ino, n, dirs, files), ino ∈ dirs ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ ispath(p + q, n, m, dirs, files) ↔ (∃ m0. ispath(p, n, m0, dirs, files) ∧ ispath(q, m0, m, dirs, files))
Proof step 12:
links(n, dirs) = ∅, ino ∈ dirs, ∃ m0. ispath(p0, ino, m0, dirs, files) ∧ ispath(str ', m0, n, dirs, files) ⊦

Rule argument

spec: <toplevel> name: path-split seq: ⊦ ispath(p + q, n, m, dirs, files) ↔ (∃ m0. ispath(p, n, m0, dirs, files) ∧ ispath(q, m0, m, dirs, files)) subst: [files, dirs, m, n, q, p] → [files, dirs, n, ino, str ', p0] flags: <all paths>

Additional information

Used terms: files, dirs, n, ino, str ', p0