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Proof step 6 from proof abs-keys-orphans (previous step)

ro.inodes?, ∀ ino. inodekey(ino) ∈ ro ↔ inodekey(ino) ∈ ri ∧ fs[ri[inodekey(ino)]].nlink = 0 ∧ ino ≠ ROOT_INO ⊦ ro = orphans(fs, ri)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ ks = ks0 ↔ (∀ key. key ∈ ks ↔ key ∈ ks0)
Proof step 8:
ro.inodes?, ∀ ino. inodekey(ino) ∈ ro ↔ inodekey(ino) ∈ ri ∧ fs[ri[inodekey(ino)]].nlink = 0 ∧ ino ≠ ROOT_INO ⊦ ∀ key. key ∈ ro ↔ key ∈ orphans(fs, ri)

Rule argument

spec: set-basic, inst: node-index name: Extension seq: ⊦ ks = ks0 ↔ (∀ key. key ∈ ks ↔ key ∈ ks0) subst: [ks0, ks] → [orphans(fs, ri), ro] flags: <all paths>

Additional information

Used terms: orphans(fs, ri), ro