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Proof step 3 from proof abs-keys-orphans (previous step)

abs-keys(ro) = abs-keys(orphans(fs, ri)), ro.inodes? ⊦ ro = orphans(fs, ri)

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:
ro.inodes?, ∀ ino. ino ∈ abs-keys(ro) ↔ ino ∈ abs-keys(orphans(fs, ri)) ⊦ ro = 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)), abs-keys(ro)] flags: <all paths>

Additional information

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