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Proof step 10 from proof inv-add4 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 11:
ro.inodes?, fo.inodes?, log-cons(log, fs), node-cons(nd6.key, nd6), node-cons(nd5.key, nd5), node-cons(nd4.key, nd4), node-cons(nd3.key, nd3), ri-cons(ri, fs), ri-inj(ri), ri-inj(fi) ⊦ adr1 = adr2, adr1 = adr3, adr1 = adr4, adr2 = adr3, adr2 = adr4, adr3 = adr4, adr4 ∈ fs, adr3 ∈ fs, adr2 ∈ fs, adr1 ∈ fs, log-cons(log, fs[adr1, nd6][adr2, nd5][adr3, nd4][adr4, nd3]) ∧ ri-cons(ri, fs[adr1, nd6][adr2, nd5][adr3, nd4][adr4, nd3])

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)