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Proof step 14 from proof keys-nodes-in-ri (previous step)

ri-cons(ri, fs), adr ∈ ri, adr ∈ ax ⊦ fs[adr].key ∈ ri

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[key] = (∅)[key]; (s) Used terms: ri, adr