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Proof step 8 from proof index-update-dom (previous step)

# ax0 = # ax1, ax0.toSet ⊆ range ri, ∀ key. key ∈ ri → ri[key] ∈ fs ∧ key-cons(key, fs[ri[key]]), ∃ adr. adr ∈ ax0 ∧ fs[adr].key = key ⊦ key ∈ ri

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information