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Proof step 23 from proof inv-add2 (previous step)

ro.inodes?, fo.inodes?, key-cons(key, fs[ri[key]]), log-cons(log, fs), node-cons(nd2.key, nd2), node-cons(nd1.key, nd1), ri-cons(ri, fs), ri-inj(ri), ri-inj(fi), key ∈ ri, ri[key] ∈ fs ⊦ adr = adr2, adr1 = adr2, key-cons(key, fs[adr1, nd2][adr2, nd1][ri[key]]), 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], nd1, adr2, fs[adr1, nd2]] 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], nd1, adr2, fs[adr1, nd2]