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Proof step 3 from proof orphans-del-dir (previous step)

# links(ino, dirs) = 0, dirs[ino] = mkdir(n, md, 0, m, ∅), afs-cons(dirs, files), ino ∈ dirs ⊦ ino = ROOT_INO, orphans(dirs -- ino, files) = orphans(dirs, files) -- ino

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ ns = ns0 ↔ (∀ ino. ino ∈ ns ↔ ino ∈ ns0)
Proof step 5:
# links(ino, dirs) = 0, dirs[ino] = mkdir(n, md, 0, m, ∅), afs-cons(dirs, files), ino ∈ dirs ⊦ ino = ROOT_INO, ∀ ino0. ino0 ∈ orphans(dirs -- ino, files) ↔ ino0 ∈ orphans(dirs, files) -- ino

Rule argument

spec: set-basic, inst: dir-heap-refset name: Extension seq: ⊦ ns = ns0 ↔ (∀ ino. ino ∈ ns ↔ ino ∈ ns0) subst: [ns0, ns] → [orphans(dirs, files) -- ino, orphans(dirs -- ino, files)] flags: <all paths>

Additional information

Used terms: orphans(dirs, files) -- ino, orphans(dirs -- ino, files)