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Proof step 3 from proof root-not-orphan (previous step)

ROOT_INO ∈ orphans(dirs, files) ⊦ # orphans(dirs, files) = 0, orphans(dirs, files) = ∅

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ ino ∈ orphans(dirs, files) ↔ valid-ino(ino, dirs, files) ∧ links(ino, dirs) = ∅ ∧ ino ≠ ROOT_INO

Rule argument

spec: <toplevel> name: orphans seq: ⊦ ino ∈ orphans(dirs, files) ↔ valid-ino(ino, dirs, files) ∧ links(ino, dirs) = ∅ ∧ ino ≠ ROOT_INO subst: [files, dirs, ino] → [files, dirs, ROOT_INO] flags: <all paths>

Additional information

Used terms: files, dirs, ROOT_INO