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Proof step 19 from proof abs-delorphans (previous step)

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 '

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 20:
links(ino, dirs) = ∅, abs(tree, ROOT_INO)(dirs), ispath(p0 + str ', ROOT_INO, ino, dirs, files), ROOT_INO ∈ dirs, ino ∈ dirs, p0 ∈ tree, str ' ∈ tree[p0], ∀ ino. ⌜ino⌝ ∈ tree.fids → ino ∈ files, ∀ ino. ¬ ino ∈ files ∨ ¬ ino ∈ dirs ⊦ # orphans(dirs, files) = 0, ino = ROOT_INO, orphans(dirs, files) = ∅

Rule argument

Additional information

Used simplifier rules: a: ⊦ (p + p0) + p1 = p + p0 + p1; from specification list[path]% ⊦ p + q ∈ tree ↔ p ∈ tree ∧ q ∈ tree[p]; (s)