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Proof step 17 from proof inv-add3 (previous step)

ro.inodes?, fo.inodes?, log-cons(log, fs), node-cons(nd3.key, nd3), node-cons(nd0.key, nd0), node-cons(nd2.key, nd2), ri-cons(ri, fs), ri-inj(ri), ri-inj(fi) ⊦ adr1 = adr2, adr1 = adr3, adr2 = adr3, adr3 ∈ fs, adr2 ∈ fs, adr1 ∈ fs, ( adr ∈ fs ∧ node-cons(fs[adr].key, fs[adr]) → adr ∈ log → node-cons(fs[adr1, nd3][adr2, nd0][adr3, nd2][adr].key, fs[adr1, nd3][adr2, nd0][adr3, nd2][adr])) ∧ (ri[key] ∈ fs ∧ key-cons(key, fs[ri[key]]) → key ∈ ri → key-cons(key, fs[adr1, nd3][adr2, nd0][adr3, nd2][ri[key]]))

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], nd2, adr3, fs[adr1, nd3][adr2, nd0]] flags: <all paths>

Additional information

Used terms: ri[key], nd2, adr3, fs[adr1, nd3][adr2, nd0]