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Proof step 7 from proof ubifs-log-nodups-add3 (previous step)

ro.inodes?, fo.inodes?, dups(log + adr0 ' + adr1 ' + adr2 '), ro ⊆ dom ri, fo ⊆ dom fi, adr2 ∈ log → adr2 ∈ fs ∧ node-cons(fs[adr2].key, fs[adr2]), ∀ adr. adr ∈ log → adr ∈ fs ∧ node-cons(fs[adr].key, fs[adr]), ∀ key. key ∈ ri → ri[key] ∈ fs ∧ node-closed(fs[ri[key]], ri, fs, ro), ∀ key. key ∈ ri → ri[key] ∈ fs ∧ key-cons(key, fs[ri[key]]) ⊦ adr0 = adr2, adr0 = adr1, adr1 = adr2, dups(log), adr2 ∈ fs, adr1 ∈ fs, adr0 ∈ fs, inodekey(0) ∈ ri

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
fo.inodes?, ro.inodes?, dups(log + adr0 ' + adr1 '), fo ⊆ dom fi, ro ⊆ dom ri, ∀ key. key ∈ ri → ri[key] ∈ fs ∧ key-cons(key, fs[ri[key]]), ∀ key. key ∈ ri → ri[key] ∈ fs ∧ node-closed(fs[ri[key]], ri, fs, ro), ∀ adr. adr ∈ log → adr ∈ fs ∧ node-cons(fs[adr].key, fs[adr]) ⊦ adr0 = adr1, adr0 = adr2, adr1 = adr2, dups(log), inodekey(0) ∈ ri, adr0 ∈ fs, adr1 ∈ fs, adr2 ∈ fs, adr2 ∈ log

Rule argument

Additional information

Used simplifier rules: a: ⊦ (ax + ax0) + ax1 = ax + ax0 + ax1; from specification list[address-list-set]%⊦ adr ≠ adr0 ∧ adr ≠ adr1 ∧ ¬ adr ∈ ax → (dups(ax + adr1 ' + adr0 ' + adr ') ↔ dups(ax + adr1 ' + adr0 ')); (s)