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Proof step 6 from proof replay-cons-strong-append (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ replay-cons-strong(fs, ri, ro, fi, fo, log) ↔ replay-safe(log, fs, fi ⊖ fo) ∧ replay(log, fs, fi, fo) = ri ⊖ ro
Proof step 8:
replay-log(log, fs, fi ⊖ fo) = ri ⊖ ro, log-cons(log, fs), node-cons(nd.key, nd), replay-safe(log, fs, fi ⊖ fo), ri-cons(ri, fs) ⊦ replay-safe(log + adr ', fs[adr, nd], fi ⊖ fo) ∧ replay(log + adr ', fs[adr, nd], fi, fo) = ri[nd.key, adr] ⊖ ro ↔ replay-one(adr, nd, ri ⊖ ro) = ri[nd.key, adr] ⊖ ro, adr ∈ fs

Rule argument

spec: <toplevel> name: replay-cons-strong seq: ⊦ replay-cons-strong(fs, ri, ro, fi, fo, log) ↔ replay-safe(log, fs, fi ⊖ fo) ∧ replay(log, fs, fi, fo) = ri ⊖ ro subst: [log, fo, fi, ro, ri, fs] → [log + adr ', fo, fi, ro, ri[nd.key, adr], fs[adr, nd]] flags: <all paths>

Additional information

Used terms: log + adr ', fo, fi, ro, ri[nd.key, adr], fs[adr, nd]