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Proof step 2 from proof nodups-new-nodups (previous step)

log-cons(log, fs), new(ax, fs) ⊦ dups(log + ax) ↔ false, dups(log), dups(ax)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
dups(log + ax), new(ax, fs), ∀ adr. adr ∈ log → adr ∈ fs ∧ node-cons(fs[adr].key, fs[adr]) ⊦ dups(ax), dups(log)

Rule argument

Additional information

Used simplifier rules: log-cons: ⊦ log-cons(log, fs) ↔ (∀ adr. adr ∈ log → adr ∈ fs ∧ node-cons(fs[adr].key, fs[adr]));