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Proof step 17 from proof abs-delorphans (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 18:
⊦ p = ε ↔ ¬(∃ p0, str. p = p0 + str ')
Proof step 19:
links(ino, dirs) = ∅, abs(tree, ROOT_INO)(dirs), ispath(p, ROOT_INO, ino, dirs, files), ROOT_INO ∈ dirs, p ∈ tree, ino ∈ dirs, ∀ ino. ¬ ino ∈ files ∨ ¬ ino ∈ dirs, ∀ ino. ⌜ino⌝ ∈ tree.fids → ino ∈ files ⊦ # orphans(dirs, files) = 0, ino = ROOT_INO, orphans(dirs, files) = ∅, ∀ p0, str. p ≠ p0 + str '

Rule argument

spec: list, inst: path name: lastdiv-rew seq: ⊦ p = ε ↔ ¬(∃ p0, str. p = p0 + str ') subst: [p] → [p] flags: <all paths>

Additional information

Used terms: p