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Proof step 12 from proof log-cons-drop (previous step)

log.toSet ∩ as = ∅, adr ∈ log, ∀ adr. adr ∈ log → adr ∈ fs ∧ node-cons(fs[adr].key, fs[adr]) ⊦ adr ∈ as, adr ∈ fs \ as ∧ node-cons((fs \ as)[adr].key, (fs \ as)[adr])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: ⊦ ¬ adr ∈ as → (fs \ as)[adr] = fs[adr]; (s)% ⊦ adr ∈ fs \ as ↔ adr ∈ fs ∧ ¬ adr ∈ as; (ws)