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Proof step 5 from proof ri-cons-key (previous step)

key-cons(key, fs[ri[key]]), key ∈ ri, ri[key] ∈ fs, ∀ key. key ∈ ri → ri[key] ∈ fs ∧ key-cons(key, fs[ri[key]]) ⊦ fs[ri[key]].key = key

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