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Proof step 9 from proof referenced-adrs-lookup-key-cons (previous step)

key-cons(fs[referenced-adrs(ax0, ri)]), ri-cons(ri, fs), adr ∈ ri ⊦ key-cons(fs[adr].key, fs[adr])

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: store+set, inst: node-index name: Data-in seq: ⊦ adr ∈ ri ↔ (∃ key. key ∈ ri ∧ ri[key] = adr) subst: [ri, adr] → [ri, adr] flags: <all paths>

Additional information

Used simplifier rules: ⊦ ri-cons(ri, fs) ∧ key ∈ ri → fs[ri[key]].key = key; (s)% ⊦ key ∈ ri ∧ ri-cons(ri, fs) → key-cons(key, fs[ri[key]]); (ss) Used terms: ri, adr