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Proof step 3 from proof path-trans (previous step)

ispath(q, n1, n2, dirs, files), ispath(p, n0, n1, dirs, files) ⊦ ispath(p + q, n0, n2, dirs, files)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ ispath(p + q, n, m, dirs, files) ↔ (∃ m0. ispath(p, n, m0, dirs, files) ∧ ispath(q, m0, m, dirs, files))
Proof step 5:
ispath(p, n0, n1, dirs, files), ispath(q, n1, n2, dirs, files) ⊦ ∃ m0. ispath(p, n0, m0, dirs, files) ∧ ispath(q, m0, n2, 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, n2, n0, q, p] flags: <all paths>

Additional information

Used terms: files, dirs, n2, n0, q, p