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Proof step 1 from proof abs-orphans-diff-datakeys (conclusion)

⊦ orphans(abs-dirs(fs, ri), abs-files(fs, ri \ datakeys(inodekey(ino), n, ri))) = orphans(abs-dirs(fs, ri), abs-files(fs, ri))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ ns = ns0 ↔ (∀ ino. ino ∈ ns ↔ ino ∈ ns0)
Proof step 3:
⊦ ∀ ino0. ino0 ∈ orphans(abs-dirs(fs, ri), abs-files(fs, ri \ datakeys(inodekey(ino), n, ri))) ↔ ino0 ∈ orphans(abs-dirs(fs, ri), abs-files(fs, ri))

Rule argument

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

Additional information

Used terms: orphans(abs-dirs(fs, ri), abs-files(fs, ri)), orphans (abs-dirs(fs, ri), abs-files(fs, ri \ datakeys(inodekey(ino), n, ri)))