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Proof step 17 from proof ubifs-log-nodups-add5 (previous step)

fo.inodes?, ro.inodes?, dups(log + adr0 ' + adr1 ' + adr2 ' + adr3 '), 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, adr0 = adr3, adr0 = adr4, adr1 = adr2, adr1 = adr3, adr1 = adr4, adr2 = adr3, adr2 = adr4, adr3 = adr4, dups(log), inodekey(0) ∈ ri, adr0 ∈ fs, adr1 ∈ fs, adr2 ∈ fs, adr3 ∈ fs, adr4 ∈ fs, adr4 ∈ log, adr3 ∈ log

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: list-dup, inst: address-list-set name: l-03 seq: ⊦ ¬ adr ∈ ax → (dups(ax + adr ') ↔ dups(ax)) subst: [adr, ax] → [adr3, log + adr0 ' + adr1 ' + adr2 '] flags: <all paths>

Additional information

Used simplifier rules: ⊦ adr ∈ ax + ax0 ↔ adr ∈ ax ∨ adr ∈ ax0; (s)% ⊦ adr ≠ adr0 → (adr ∈ adr0 ' + ax ↔ adr ∈ ax); (s)% ⊦ adr ∈ adr0 ' ↔ adr = adr0; (s)%a: ⊦ (ax + ax0) + ax1 = ax + ax0 + ax1; from specification list[address-list-set] Used terms: adr3, log + adr0 ' + adr1 ' + adr2 '