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Proof step 15 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 ∈ fs, adr ∈ log

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 16:
⊦ ¬ adr ∈ ri → ¬ adr ∈ ri ⊖ ks
Proof step 17:
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, adr ∈ ri ⊖ ro ⊦ adr ∈ log, adr ∈ fs

Rule argument

spec: aubifs-base name: notin-dels seq: ⊦ ¬ adr ∈ ri → ¬ adr ∈ ri ⊖ ks subst: [ks, ri, adr] → [ro, ri, adr] flags: <all paths>

Additional information

Used terms: ro, ri, adr