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Proof step 42 from proof inv-add4 (previous step)

ro.inodes?, fo.inodes?, key-cons(key, fs[ri[key]]), log-cons(log, fs), node-cons(nd6.key, nd6), node-cons(nd5.key, nd5), node-cons(nd4.key, nd4), node-cons(nd3.key, nd3), ri-cons(ri, fs), ri-inj(ri), ri-inj(fi), key ∈ ri, ri[key] ∈ fs ⊦ adr1 = adr2, adr1 = adr3, adr1 = adr4, adr2 = adr3, adr2 = adr4, adr3 = adr4, key-cons(key, fs[adr1, nd6][adr2, nd5][ri[key]]), adr4 ∈ fs, adr3 ∈ fs, adr2 ∈ fs, adr1 ∈ fs

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: store, inst: node-store name: At-other seq: ⊦ adr ≠ adr0 → fs[adr0, nd][adr] = fs[adr] subst: [adr, nd, adr0, fs] → [ri[key], nd5, adr2, fs[adr1, nd6]] flags: <all paths>

Additional information

Used simplifier rules: ⊦ adr ∈ fs ∧ ¬ adr0 ∈ fs → fs[adr0, nd][adr] = fs[adr]; (s)% ⊦ key ∈ ri ∧ ri-cons(ri, fs) → key-cons(key, fs[ri[key]]); (ss) Used terms: ri[key], nd5, adr2, fs[adr1, nd6]