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Proof step 6 from proof expath-split (previous step)

ispath(p + q, ino, m, dirs, files) ⊦ ∃ m. ispath(p, ino, m, dirs, files) ∧ ispath(q, m, dirs, files)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ ispath(p + q, n, m, dirs, files) ↔ (∃ m0. ispath(p, n, m0, dirs, files) ∧ ispath(q, m0, m, dirs, files))
Proof step 8:
∃ m0. ispath(p, ino, m0, dirs, files) ∧ ispath(q, m0, m, dirs, files) ⊦ ∃ m. ispath(p, ino, m, dirs, files) ∧ ispath(q, m, 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, m, ino, q, p] flags: <all paths>

Additional information

Used terms: files, dirs, m, ino, q, p