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Proof step 31 from proof inv-add5 (previous step)

ro.inodes?, fo.inodes?, log-cons(log, fs), node-cons(nd7.key, nd7), node-cons(nd6.key, nd6), node-cons(nd1.key, nd1), node-cons(nd5.key, nd5), node-cons(nd4.key, nd4), ri-cons(ri, fs), ri-inj(ri), ri-inj(fi) ⊦ adr1 = adr5, adr1 = adr4, adr1 = adr3, adr1 = adr2, adr2 = adr5, adr2 = adr4, adr2 = adr3, adr3 = adr5, adr3 = adr4, adr4 = adr5, ri-cons(ri, fs[adr1, nd7][adr2, nd6][adr3, nd1][adr4, nd5][adr5, nd4]), adr1 ∈ fs, adr2 ∈ fs, adr3 ∈ fs, adr4 ∈ fs, adr5 ∈ fs

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 32:
fo.inodes?, ro.inodes?, key-cons(key, fs[ri[key]]), log-cons(log, fs), node-cons(nd4.key, nd4), node-cons(nd5.key, nd5), node-cons(nd1.key, nd1), node-cons(nd6.key, nd6), node-cons(nd7.key, nd7), ri-cons(ri, fs), ri-inj(fi), ri-inj(ri), key ∈ ri, ri[key] ∈ fs ⊦ adr1 = adr2, adr1 = adr3, adr1 = adr4, adr1 = adr5, adr2 = adr3, adr2 = adr4, adr2 = adr5, adr3 = adr4, adr3 = adr5, adr4 = adr5, key-cons(key, fs[adr1, nd7][adr2, nd6][adr3, nd1][adr4, nd5][adr5, nd4][ri[key]]), adr5 ∈ fs, adr4 ∈ fs, adr3 ∈ fs, adr2 ∈ fs, adr1 ∈ fs

Rule argument

Additional information

Used simplifier rules: ⊦ adr ∈ fs[adr1, nd] ↔ adr = adr1 ∨ adr ∈ fs; (s)%⊦ ri-cons(ri, fs) → ( ri-cons(ri0, fs0) ↔ (∀ key. (key ∈ ri → ri[key] ∈ fs ∧ key-cons(key, fs[ri[key]])) → key ∈ ri0 → ri0[key] ∈ fs0 ∧ key-cons(key, fs0[ri0[key]]))); (ss)