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Proof step 2 from proof abs-orphans (previous step)

afs-cons(abs-dirs(fs, ri), abs-files(fs, ri)) ⊦ orphans(abs-dirs(fs, ri), abs-files(fs, ri)) = abs-keys(orphans(fs, ri))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ ns = ns0 ↔ (∀ ino. ino ∈ ns ↔ ino ∈ ns0)
Proof step 4:
afs-cons(abs-dirs(fs, ri), abs-files(fs, ri)) ⊦ ∀ ino. ino ∈ orphans(abs-dirs(fs, ri), abs-files(fs, ri)) ↔ ino ∈ abs-keys(orphans(fs, ri))

Rule argument

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

Additional information

Used terms: abs-keys(orphans(fs, ri)), orphans(abs-dirs(fs, ri), abs-files(fs, ri))