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Proof step 18 from proof replay-cons-strong-append (previous step)

replay-log(log, fs, fi ⊖ fo) = ri ⊖ ro, replay-one(adr, nd, ri ⊖ ro) = ri[nd.key, adr] ⊖ ro, log-cons(log, fs), node-cons(nd.key, nd), replay-safe(log, fs, fi ⊖ fo), ri-cons(ri, fs), adr ∈ ri ⊖ ro, adr ∈ ri ⊦ adr ∈ fs, adr ∈ log

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: ⊦ key ∈ ri ∧ ri-cons(ri, fs) → ri[key] ∈ fs; (ss) Used terms: ri, adr