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Proof step 44 from proof recovery (previous step)

⌜ino0⌝ ∈ fs ↔ links(ino0, dirs0) ≠ ∅ ∧ ino0 ∈ files1, tree0.dir?, dom of1 < ino, abs(tree0, ROOT_INO)(dirs0), afs-cons(dirs0, files1), afs-cons(dirs0, files1 \ orphans(dirs0, files1)), fids-cons(tree0, abs-files(files1), abs-of(of1)), of-cons(of1, dirs0, files1), of-cons(∅, dirs0, files1 \ orphans(dirs0, files1)), ⌜ino0⌝ ∈ fs → fs[⌜ino0⌝ ] = abs-files(files1)[⌜ino0⌝ ], ∀ ino. ⌜ino⌝ ∈ tree0.fids → ino ∈ files1 ⊦ (⌜ino0⌝ ∈ fs ↔ ino0 ∈ files1 ∧ ¬ ino0 ∈ orphans(dirs0, files1)) ∧ (⌜ino0⌝ ∈ fs → fs[⌜ino0⌝ ] = abs-files(files1 \ orphans(dirs0, files1))[⌜ino0⌝ ])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 45:
⊦ ino ∈ orphans(dirs, files) ↔ valid-ino(ino, dirs, files) ∧ links(ino, dirs) = ∅ ∧ ino ≠ ROOT_INO
Proof step 46:
⌜ino0⌝ ∈ fs ↔ links(ino0, dirs0) ≠ ∅ ∧ ino0 ∈ files1, tree0.dir?, dom of1 < ino, abs(tree0, ROOT_INO)(dirs0), afs-cons(dirs0, files1 \ orphans(dirs0, files1)), afs-cons(dirs0, files1), fids-cons(tree0, abs-files(files1), abs-of(of1)), of-cons(∅, dirs0, files1 \ orphans(dirs0, files1)), of-cons(of1, dirs0, files1), ⌜ino0⌝ ∈ fs → fs[⌜ino0⌝ ] = abs-files(files1)[⌜ino0⌝ ], ∀ ino. ⌜ino⌝ ∈ tree0.fids → ino ∈ files1 ⊦ (⌜ino0⌝ ∈ fs ↔ ino0 ∈ files1 ∧ ¬(valid-ino(ino0, dirs0, files1) ∧ links(ino0, dirs0) = ∅ ∧ ino0 ≠ ROOT_INO)) ∧ (⌜ino0⌝ ∈ fs → fs[⌜ino0⌝ ] = abs-files(files1 \ orphans(dirs0, files1))[⌜ino0⌝ ])

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] → [files1, dirs0, ino0] flags: <all paths>

Additional information

Used terms: files1, dirs0, ino0