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Proof step 7 from proof log-cons-app (previous step)

⊦ (∀ adr. adr ∈ log0 + log1 → adr ∈ fs ∧ node-cons(fs[adr].key, fs[adr])) ↔ (∀ adr. adr ∈ log0 → adr ∈ fs ∧ node-cons(fs[adr].key, fs[adr])) ∧ (∀ adr. adr ∈ log1 → adr ∈ fs ∧ node-cons(fs[adr].key, fs[adr]))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: a: ⊦ (ax + ax0) + ax1 = ax + ax0 + ax1; from specification list[address-list-set]% ⊦ adr ∈ ax + ax0 ↔ adr ∈ ax ∨ adr ∈ ax0; (s)