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Proof step 37 from proof inv-add4 (previous step)

fo.inodes?, ro.inodes?, log-cons(log, fs), node-cons(nd3.key, nd3), node-cons(nd4.key, nd4), node-cons(nd5.key, nd5), node-cons(nd6.key, nd6), node-cons(fs[adr].key, fs[adr]), ri-cons(ri, fs), ri-inj(fi), ri-inj(ri), adr ∈ log, adr ∈ fs ⊦ ri[key] = adr4, adr1 = adr4, adr1 = ri[key], adr1 = adr2, adr2 = adr4, adr2 = ri[key], node-cons(fs[adr1, nd6][adr2, nd5][adr].key, fs[adr1, nd6][adr2, nd5][adr]), adr1 ∈ fs, adr2 ∈ fs, ri[key] ∈ fs, adr4 ∈ 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] → [adr, nd5, adr2, fs[adr1, nd6]] flags: <all paths>

Additional information

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