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Proof step 9 from proof inv-add5 (previous step)

adr = adr11, adr0 = adr10, adr6 = adr9, adr7 = adr12, adr8 = adr13, nd = nd4, nd0 = nd5, nd2 = nd6, nd3 = nd7, ro.inodes?, fo.inodes?, log-cons(log, fs), new(adr1 ' + adr2 ' + adr3 ' + (adr4 ' + adr5), 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) ⊦ dups(adr1 ' + adr2 ' + adr3 ' + adr4 ' + adr5 '), log-cons(((((log + adr1) + adr2) + adr3) + adr4) + adr5, fs[adr1, nd3][adr2, nd2][adr3, nd1][adr4, nd0][adr5, nd]) ∧ ri-cons(ri, fs[adr1, nd3][adr2, nd2][adr3, nd1][adr4, nd0][adr5, nd])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
fo.inodes?, ro.inodes?, 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) ⊦ adr1 = adr2, adr1 = adr3, adr1 = adr4, adr1 = adr5, adr2 = adr3, adr2 = adr4, adr2 = adr5, adr3 = adr4, adr3 = adr5, adr4 = adr5, adr5 ∈ fs, adr4 ∈ fs, adr3 ∈ fs, adr2 ∈ fs, adr1 ∈ fs, log-cons(log, fs[adr1, nd7][adr2, nd6][adr3, nd1][adr4, nd5][adr5, nd4]) ∧ ri-cons(ri, fs[adr1, nd7][adr2, nd6][adr3, nd1][adr4, nd5][adr5, nd4])

Rule argument

Additional information

Used simplifier rules: ⊦ fs[adr, nd][adr] = nd; (s)% ⊦ adr ≠ adr0 → fs[adr0, nd][adr] = fs[adr]; (s)% ⊦ adr ∈ fs[adr1, nd] ↔ adr = adr1 ∨ adr ∈ fs; (s)% ⊦ adr ≠ adr0 → (adr ∈ fs[adr0, nd] ↔ adr ∈ fs); (s)% ⊦ log-cons(adr ', fs) ↔ adr ∈ fs ∧ node-cons(fs[adr].key, fs[adr]); (s)% ⊦ log-cons(log0 + log1, fs) ↔ log-cons(log0, fs) ∧ log-cons(log1, fs); (s)% ⊦ dups(adr ' + adr0 ') ↔ adr = adr0; (s)% ⊦ adr ∈ adr0 ' ↔ adr = adr0; (s)% ⊦ adr ∈ adr0 ' + ax ↔ adr = adr0 ∨ adr ∈ ax; (s)% ⊦ dups(adr ' + ax) ↔ adr ∈ ax ∨ dups(ax); (s)% ⊦ dups(adr ' + ax) ↔ dups(ax) ∨ adr ∈ ax; (ws)% ⊦ new(adr ', fs) ↔ ¬ adr ∈ fs; (s)% ⊦ new(adr ' + log, fs) ↔ ¬ adr ∈ fs ∧ new(log, fs); (s)%a: ⊦ (ax + ax0) + ax1 = ax + ax0 + ax1; from specification list[address-list-set]% ⊦ ax + adr = ax + adr '; (s)