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Proof step 19 from proof index-update-dom (previous step)

# ax0 = # ax1, key-cons(key, fs[ri[key]]), key ∈ ri, ri[key] ∈ ax0, ri[key] ∈ fs ⊦ fs[ri[key]].key ∈ ri

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: key-cons seq: ⊦ key-cons(key, nd) ↔ nd.key = key ∧ (key.inode? → nd.inode? ∧ key.ino ≠ 0) ∧ (key.dentry? → nd.dentry?) ∧ (key.data? → nd.data?) subst: [nd, key] → [fs[ri[key]], key] flags: <all paths>

Additional information

Used terms: fs[ri[key]], key