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Proof step 6 from proof abs-delorphans (previous step)

abs(tree, ROOT_INO)(dirs), ino ∈ dirs, ino ∈ orphans(dirs, files), ∀ ino. ⌜ino⌝ ∈ tree.fids → ino ∈ files, ∀ ino. ¬ ino ∈ files ∨ ¬ ino ∈ dirs ⊦ # orphans(dirs, files) = 0, orphans(dirs, files) = ∅

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ ino ∈ orphans(dirs, files) ↔ valid-ino(ino, dirs, files) ∧ links(ino, dirs) = ∅ ∧ ino ≠ ROOT_INO
Proof step 8:
links(ino, dirs) = ∅, abs(tree, ROOT_INO)(dirs), valid-ino(ino, dirs, files), ino ∈ dirs, ∀ ino. ¬ ino ∈ files ∨ ¬ ino ∈ dirs, ∀ ino. ⌜ino⌝ ∈ tree.fids → ino ∈ files ⊦ # orphans(dirs, files) = 0, ino = ROOT_INO, orphans(dirs, files) = ∅

Rule argument

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

Additional information

Used terms: files, dirs, ino